Answer:
The Inequality to determine the number of tickets the committee could sell to pay this years dance [tex]72+4t\geq 400[/tex].
The committee need to sell more than 82 tickets to have money left over after they pay this years dance.
Step-by-step explanation:
Given:
Cost of the Dance =$400
Money earn from bake sale =$72
Cost of each ticket = $4
We need write the inequality to determine the number of tickets the committee could sell to pay this years dance.
Solution:
Let the number of tickets to be sell be 't'.
So we can say that;
Money earn from bake sale plus Cost of each ticket multiplied by number of tickets should be greater than or equal to Cost of the Dance.
framing in equation form we get;
[tex]72+4t\geq 400[/tex]
Hence The Inequality to determine the number of tickets the committee could sell to pay this years dance [tex]72+4t\geq 400[/tex].
On solving the above equation we get;
subtracting both side by 72 we get;
[tex]72+4t-72\geq 400-72\\\\4t\geq 328[/tex]
Dividing both side by 4 we get;
[tex]\frac{4t}{4}\geq \frac{328}{4}\\\\t\geq 82[/tex]
Hence The committee need to sell more than 82 tickets to have money left over after they pay this years dance.
Find the area of a regular octagon with a side length of 10 cm. Round to the nearest tenth.
The question keeps telling me to STOP! Never mind.
The octagon is 8 isosceles triangles. Each has common side r and base 10. The central angle is 360/8 = 45°. By the Law of cosines,
10² = r² + r² - 2 r² cos 45° = 2r²(1 - √2/2) = r²(2-√2)
r² = 100/(2-√2)
The area of a triangle with sides a,b and included angle C is (1/2)ab sin C. Our 8 octagon isosceles triangles each have sides r and r and included angle 45° so our total area, 8 triangles, is
A = 8(1/2) r² sin 45° = (400/(2-√2)) (√2/2) × (2+√2)/(2+√2) = 200(1+√2)
A ≈482.84271
Answer: 482.8 sq cm
Final answer:
To find the area of a regular octagon with a side length of 10 cm, use the formula: Area = 2 * (1 + √2) * side length². Substitute the given side length and round the answer to the nearest tenth.
Explanation:
To find the area of a regular octagon with a side length of 10 cm, we can use the formula:
Area = 2 * (1 + √2) * side length²
Substituting the given side length into the formula:
Area = 2 * (1 + √2) * (10)²
Area = 2 * (1 + √2) * 100
Area ≈ 414.2 cm² (rounded to the nearest tenth)
After further computation, the area approximates 414.2 cm², rounded to the nearest tenth. This formula captures the geometric intricacies of a regular octagon, demonstrating a concise method to calculate its area based on the given side length. This formula encapsulates the unique characteristics of a regular octagon, providing a streamlined approach to computing its area and showcasing the elegant relationship between side length and the polygon's spatial coverage.
URGENT PLZZZ!!!! for the given situation identify the independent and dependent variables and then find a reasonable domain and range of values. Listed below will be four statements that relate to the given situation. She’s the statement that would have to be false given the situation and it’s parameters.
chain owns a scooter that can travel 65 miles per gallon of gasoline. her tank holds 2.5 gallons. She’s planning on taking a shopping trip around her city.
here are the statements
1) The range is 0 miles to 162.5 miles
2) The dependent variable is how many hours she will spend shopping in the stores
3) The independent variable is how much gasoline she’ll use
4) The domain is 2.5 gallons to 0 gallons
Answer:
2
Step-by-step explanation:
the dependent variable is the amount of time she spends driving around.
Final answer:
In the scenario, the independent variable is the amount of gasoline used, and the dependent variable is the distance traveled. The domain is 0 to 2.5 gallons and the range is 0 to 162.5 miles, hence statement 2 is false regarding the dependent variable.
Explanation:
For the given situation, the independent variable is the amount of gasoline she'll use. This is because it is the variable that can be changed freely and does not depend on the other variables in the situation. In contrast, the dependent variable is the distance that can be traveled with the scooter, as it depends on the amount of gasoline used.
The domain for this situation would be the amount of gasoline available for use, which is between 0 gallons (an empty tank) and 2.5 gallons (a full tank). The range would be the distance the scooter can travel on that gasoline, from 0 miles (no gasoline) to 162.5 miles (2.5 gallons at 65 miles per gallon).
Therefore, statement 2 "The dependent variable is how many hours she will spend shopping in the stores" would have to be false given the situation and its parameters, because the dependent variable is actually the distance that can be traveled, not the time spent shopping.
Supriya is decorating her bedroom. She plans to hang strings of twinkle lights all the way around her walls. She measures the walls and finds she will need 36 meters of lights. Which measurement did Supriya find?
Answer:
Perimeter
Step-by-step explanation:
Perimeter is the distance all round a particular shape. Since we are not given the shape of her bedroom, we may not have a particular formula that was uses to find the perimeter. Despite all that, the only way that she could arrive to conclusion that 36 meters of light are needed, then Supriya it is by finding the perimeter.
Suppose you order an ice cream cone that holds 157 cubic centimeters of your favorite flavor. You calculate the height of your cone is 12cm. Find the diameter of your ice cream cone. (Use π≈3.14, and round to the nearest hundredth.)
Answer: Diameter = 7.06 cm
Step-by-step explanation:
The formula for determining the volume of a cone is expressed as
Volume = 1/3πr²h
Where
h represents the height of the cone
r represents the radius of the cone
π is a constant whose value is 3.14
From the information given
Volume = 157 cubic centimeters
Height = 12cm
Therefore,
157 = 1/3 × 3.14 × r² × 12
157 =12.56r²
r² = 157/12.56
r² = 12.5
Taking square root of both sides of the equation, it becomes
r = √12.5
r = 3.53 cm
Diameter = 2 × radius = 2 × 3.53
Diameter = 7.06 cm
WILL GIVE BRAINLIEST!!!
Answer:
B.
Step-by-step explanation:
Answers A, D, C dont make any sense to me
PLZZ BRAINLIEST
Which point lies on the circle represented by the equation (x + 5)2 + (-9)2 = 82?
A. (0,8)
B. (13,-9)
c. (-5,1)
D. (3,17)
Answer:
None of the given points lies on the circle.
Step-by-step explanation:
The circle is represented by the following formula:
(x - xc)² + (y - yc)² = r²
Where (xc,yc) are the coordinates of the center and r is the radius of the circle. In the case we have:
(x+5)² + (y-9)² = 82
If a point belongs to this circumference, then the results of applying the points to the equation should be valid. To test all the points we are going to apply each to the equation as shown below:
A.
(0 + 5)² + (8-9)² = 82
5² + (-1)² = 82
25 + 1 = 82
26 = 82 (invalid)
The point does not lies on the circle.
B.
(13 + 5)² + (-9-9)² = 82
(18)² + (-18)² = 82
324 + 324 = 82
648 = 82 (invalid)
The point does not lies on the circle.
C.
(-5 + 5)² + (1 - 9)² = 82
0² + (-8)² = 82
64 = 82 (invalid)
The point does not lies on the circle.
D.
(3 + 5)² + (17-9)² = 82
8² + 8² = 82
64 + 64 = 82
128 = 82 (invalid)
The point does not lies on the circle.
Answer:
c
Step-by-step explanation:
1. 70% of 7 =
2. 30% of 134 =
3. 100% of 109 =
4. 60% of 112 =
40% of 142 =
6. 20% of 89 =
7. 10% of 127 =
8. 80% of 7 =
9. 90% of 95 =
10. 90% of 7 =
11. 80% of 154 =
12. 10% of 2 =
13. 100% of 2 =
14. 30% of 76 =
15. 70% of 43 =
Answer:
1. 70% of 7 = 4.9
2. 30% of 134 = 40.2
3. 100% of 109 = 109
4. 60% of 112 = 67.2
5. 40% of 142 = 56.8
6. 20% of 89 = 17.8
7. 10% of 127 = 12.7
8. 80% of 7 = 5.6
9. 90% of 95 = 85.5
10. 90% of 7 = 6.3
11. 80% of 154 = 123.2
12. 10% of 2 = 0.2
13. 100% of 2 = 2
14. 30% of 76 = 22.8
15. 70% of 43 = 30.1
Step-by-step explanation:
1. I
2. USED
3. GOOGLE
You're welcome! <3
1015
© 5 t-shirts and a hat costs £27.00
2 t-shirts and a hat costs £12.00.
How much does a t-shirt cost?
How much does a hat cost?
t-shirt: £
hat: £
Answer:
A shirt cost £5 while the hat cost £2.
Step-by-step explanation:
What I did was guess and check until i found the amount of each item. You can also use a table to this.
What is the solution to the equation 2 2/5 + r = 5 2/5 ?
r = 7
r = 3
r = 3
r = 3
Answer: [tex]r=3[/tex]
Simplify both sides of the equation
[tex]r+12/5=27/5[/tex]
Subtract 12/5 from both sides
[tex]r+12/5-12/5=27/5-12/5[/tex]
[tex]r=3[/tex]
The solution to the equation 2 2/5 + r = 5 2/5 is r = 3, which is found by subtracting 2 2/5 (converted to 12/5) from 5 2/5 (converted to 27/5).
Explanation:The solution to the equation 2 2/5 + r = 5 2/5 is found by isolating the variable r.
First, convert the mixed numbers to improper fractions.
We have 12/5 (equivalent to 2 2/5) and 27/5 (equivalent to 5 2/5).
Now, subtract 12/5 from both sides of the equation to get r on one side:
27/5 - 12/5 = rAfter subtraction, we find that:
r = 15/5r = 3Thus, the solution to the equation is r = 3.
What are two numbers that are the same equal to 28
Answer:
2 and 14?
Step-by-step explanation:
Multiplied together they are 28, but I don't know if that's what you were asking
I wanna know: [3,5]={3,4,5}? Why?
Answer:
Yes if [3,5] is a set of integers then it contains elements 3,4,5
As Closed bracket denotes that extreme points are also included and 4 is mid element in between 3 and 5
Angle x and y are complementary. Angle x is supplementary to a 128º angle.
What are the measures of angle x and angle y?
Answer:
x = 52
y = 38
Step-by-step explanation:
Angle x is supplementary to a 128º angle.
Supplementary angles add to 180
x+128 = 180
Subtract 128 from each side
x+128-128 = 180-128
x =52
Angle x and y are complementary.
Complementary angles add to 90
x+y =90
52+y =90
Subtract 52 from each side
52-52 +y = 90-52
y = 38
Answer:
x = 52°
y = 38°
Step-by-step explanation:
x = 180 - 128
x = 52
y = 90 - 52 = 38
>What would the new point be if you rotated the point (4,9) 180°about the origin?
Answer:(-4,-9)
Step-by-step explanation:
Final answer:
After rotating the point (4,9) 180° about the origin, the new coordinates would be (-4, -9).
Explanation:
To determine the new coordinates of a point after a 180° rotation about the origin, you can apply the rules of rotation in a coordinate plane.
For a 180° rotation, each coordinate (x, y) becomes (-x, -y).
Therefore, if we rotate the point (4,9) 180° about the origin, we change the sign of both coordinates.
The new point after rotation would be (-4, -9).
What is the equation of the line with the same slope as the equation x-4y=3 and the y-intercept(0,-8)?
Answer:
y = 1/4x -8
Step-by-step explanation:
First find the slope of the line
x-4y =3
Subtract x from each side
x-4y -x = -x+3
-4y = -x+3
Divide each side by -4
-4y/-4 = -x/-4 +3/-4
y = 1/4 x -3/4
This is in the form y= mx+b where the slope is m and the y intercept is b
The slope is 1/4
We want the same slope
y = 1/4x +b
we know the y intercept is -8
y = 1/4x -8
What is the distance between (8,1) and (9,1)?
Answer:
1
Step-by-step explanation:
9-8=1
since it is on the same y coordinate it doesn't move much
John runs 15 miles in 3 hours. How many miles can John run per hour?
Answer:
5 yeet
Step-by-step explanation:
Todd earned some money doing chores. He spent one-fourth of his money see a movie. Then he spent $6.00 on popcorn and drinks. When he went home, he had $24.00 left. How much did Todd earn mowing the neighbor's lawn?
Answer: Todd earned $40 mowing the neighbor's lawn.
Step-by-step explanation:
Let x represent the amount of money that Todd earned, mowing his neighbor's lawn.
He spent one-fourth of his money see a movie. It means that the amount spent in seeing a movie is x/4
Then he spent $6.00 on popcorn and drinks. It means that the total amount spent is
x/4 + 6
The amount left would be
x - (x/4 + 6) = x - x/4 - 6
When he went home, he had $24.00 left. It means that
x - x/4 - 6 = 24
x - x/4 = 24 + 6
x - x/4 = 30
Cross multiplying by 4, it becomes
4x - x = 120
3x = 120
x = 120/3
x = $40
Answer: 40$ got it right on edge :)
Step-by-step explanation:
the circumference of a circle c with a radius of r units is approximately given by the linear equation C=6.3r. Find two solutions of this function. Explain the solutions.
Final answer:
The circumference of a circle with a given radius can be calculated using the linear equation C = 6.3r. Two examples of solutions to this equation are C = 12.6 units when r = 2, and C = 31.5 units when r = 5.
Explanation:
The circumference of a circle with a radius of r units is given by the linear equation C = 6.3r. To find two solutions of this function, we can substitute different values for r into the equation.
For example, if we let r = 2, then the circumference C is calculated as C = 6.3 * 2 = 12.6 units.
Another solution is when r = 5. In this case, the circumference C is C = 6.3 * 5 = 31.5 units.
A survey finds customers are charged incorrectly for 4 out of every 10 items. suppose a customer purchases 11 items. find the probability that the customer is charged incorrectly on at least 3 items. the probability that the customer is charged incorrectly on at least 3 items is nothing
Answer:
The probability that the customer is charged incorrectly on at least 3 items is 88.11%
Step-by-step explanation:
For each item, there are only two possible outcomes. Either they are charged correctly, or they are not. The probability of an item being charged incorrectly is independent of other items. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A survey finds customers are charged incorrectly for 4 out of every 10 items.
This means that [tex]p = \frac{4}{10} = 0.4[/tex]
Suppose a customer purchases 11 items.
This means that [tex]n = 11[/tex]
Find the probability that the customer is charged incorrectly on at least 3 items.
Either he is charged incorrectly on less than 3 items, or at least 3. The sum of the probabilities of these events is decimal 1. So
[tex]P(X < 3) + P(X \geq 3) = 1[/tex]
We want [tex]P(X \geq 3)[/tex]. So
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{11,0}.(0.4)^{0}.(0.6)^{11} = 0.0036[/tex]
[tex]P(X = 1) = C_{11,1}.(0.4)^{1}.(0.6)^{10} = 0.0266[/tex]
[tex]P(X = 2) = C_{11,2}.(0.4)^{2}.(0.6)^{9} = 0.0887[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0036 + 0.0266 + 0.0887 = 0.1189[/tex]
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.1189 = 0.8811[/tex]
88.11% probability that the customer is charged incorrectly on at least 3 items
Final answer:
To determine the probability that a customer is charged incorrectly on at least three items out of 11, we use the binomial probability formula, summing up probabilities from 3 to 11 incorrect charges.
Explanation:
Probability of Being Charged Incorrectly on At Least 3 Items
To solve the problem of finding the probability that a customer is charged incorrectly on at least three items when they purchase 11 items, we use the binomial probability formula. Given that the probability of being charged incorrectly for one item is 0.4 (4 out of 10), we denote this as p=0.4. The probability of being charged correctly is q=1-p=0.6. The total number of items, n, is 11.
The binomial probability P(X ≥ k) for at least k successes out of n trials is calculated by summing up the probabilities of having k, k+1,..., n successes.
To find P(X ≥ 3) we calculate:
P(X=3) where X represents the number of items charged incorrectlyContinue similarly to find P(X=4), P(X=5), ..., P(X=11)Sum these probabilities to get P(X ≥ 3)This calculation involves using the binomial formula which is:
P(X=k) = C(n,k) × p^k × q^(n-k)
Where C(n,k) is the combination of n items taken k at a time.
Once each individual probability is calculated, add them up to find the total probability of being charged incorrectly on at least 3 items. Remember, it is not possible to have a probability greater than 1, as this would imply certainty beyond the maximum possible (100%).
To rent a boat it costs 11$ plus an additional 10$ per hour if you have 71$ write and solve an equation to solve an equation to determine how many hours you can rent the boat
HURRRY PLEASE N HELP
Coach McGee uses the
table to show her team's current basketball shot average compared to previous years,
2010
2008
-5.8
2009
4.4
10
-
2012
2013
2011
3.6
Which comparison is true? Use the number line to help you.
-6 -5 -4 -3 -2 -1 0
1 2 3 4 5 6
0 -5.8>-53
Answer:
b
Step-by-step explanation:
Answer:
the answer is B
Step-by-step explanation
hope it helps!
Darnell's baseball team always does warm-ups before a game. Before last week's game, Darnell did 50 knee lifts in 2 minutes. Today, he will do knee lifts for 3 minutes.
If he does them at the same rate, how many knee lifts will Darnell do today?
Answer:
Darnell will do 75 knee lifts
Step-by-step explanation:
in two minutes he did 50. So that means that in one minute he did 25. add 50 and 25 together and you get 75 for your answer
Answer:75 knee lifts
Step-by-step explanation:2 mins 50 knee lifts
1 min 25 knee lifts
A swimming pool is to be drained. The pool is shaped like a rectangular prism with length 30 feet, wide 18 ft, and depth 4ft. Suppose water is pumped out of the pool at a rate of 216ft3 per hour. If the pool starts completely full, how many hours does it take to empty the pool?
Answer: it will take 9 hours to empty the pool.
Step-by-step explanation:
The pool is shaped like a rectangular prism with length 30 feet, wide 18 ft, and depth 4ft. It means that when the pool is full, its volume is
30 × 18 × 4 = 2160 ft³
If water is pumped out of the pool at a rate of 216ft3 per hour, then the rate at which the water in the pool is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + d(n - 1)
Where
a represents the first term of the sequence(initial amount of water in the pool when completely full).
d represents the common difference(rate at which it is being pumped out)
n represents the number of terms(hours) in the sequence.
From the information given,
a = 2160 degrees
d = - 216 ft3
Tn = 0(the final volume would be zero)
We want to determine the number of terms(hours) for which Tn would be zero. Therefore,
0 = 2160 - 216 (n - 1)
2160 = 216(n - 1) = 216n + 216
216n = 2160 - 216
216n = 1944
n = 1944/216
n = 9
Step-by-step explanation:
Answer: it will take 9 hours to empty the pool. Step-by-step explanation: The pool is shaped like a rectangular prism with length 30 feet, wide 18 ft, and depth 4ft. It means that when the pool is full, its volume is 30 x 18 x 4 = 2160 ft3 If water is pumped out of the pool at a rate of 216ft3 per hour, then the rate at which the water in the pool is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as Tn = a + d(n - 1) Where a represents the first term of the sequence(initial amount of water in the pool when completely full). d represents the common difference(rate at which it is being pumped out) n represents the number of terms(hours) in the sequence. From the information given, a = 2160 degrees 216 ft3 d = Tn = 0(the final volume would be zero) We want to determine the number of terms(hours) for which Tn would be zero.
We want to determine the number of terms(hours) for which Tn would be zero. Therefore,
O = 2160 - 216 (n - 1) 2160 = 216(n - 1) = 216n + 216 216n = 2160 - 216 216n = 1944 %3D n = 1944/216 n = 9
3x + y = -1
2x + 3y = 18
Answer: [tex]x=-3\\y=8[/tex]
Step-by-step explanation:
[tex]3x+y=-1\\2x+3y=18[/tex]
Multiply by -3 the upper equation to make y equal in value but with opposite signs.
[tex](-3)(3x+y=-1)\\-9x-3y=3[/tex]
Now add equation 1 and 2.
[tex]-9x-3y=3\\2x+3y=18[/tex]
--------------------------
[tex]-7x=21[/tex]
Solve for x;
To isolate x, divide by -7
[tex]\frac{-7x}{-7}=\frac{21}{-7}[/tex]
[tex]x=-3[/tex]
Now use one of the equations above and replace the value of x.
[tex]3x+y=-1\\3(-3)+y=-1\\-9+y=-1\\y=-1+9\\y=8[/tex]
To prove if it's correct, take either equation and replace both x and y values, if the results are equal to each other, it is correct.
[tex]2x+3y=18\\2(-3)+3(8)=18\\-6+24=18\\18=18[/tex]
Find the m∠ARG in rhombus RAGL, given that m∠RAG = 58°.
Step-by-step explanation:
RAGL is a rhombus.
[tex] \therefore RA = AG..
(sides\: of\: rhombus) \\
\therefore m\angle ARG = m\angle AGR... (1)[/tex]
(Angles opposite to equal sides are equal)
[tex] In\:\triangle RAG, \\
m\angle ARG +\bold{ m\angle AGR} + {m\angle RAG} = 180°\\
m\angle ARG +\bold {m\angle ARG} + 58° = 180°\\
[From\:equation \: (1)]\\
2m\angle ARG = 180°-58° \\
2m\angle ARG = 122° \\
m\angle ARG =\frac{122°}{2} \\
\huge \red {\boxed {m\angle ARG = 61°}} [/tex]
Hence, option A is the correct answer.
One letter was selected at random from the words San Antonio. What is the probability that the selected letter was either an a or an n
The required probability of the selected letter was either an a or an n is 0.5.
Given that,
One letter was selected at random from the words San Antonio. The probability that the selected letter was either an a or an n is to be determined.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Total letters = 10
Total a and n = 2 and 3
The probability is given as = 2 / 10 + 3 / 10
= 5/10 = 1/2 = 0.5
Thus, the required probability of the selected letter was either an a or an n is 0.5.
Learn more about probability here:
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PLEASE HELP ME WILL GIVE 20 POINTS The growth of two varieties of plant after 20 days is shown. Construct a back-to-back stem and leaf plot for the data.
Variety 1
20 12 39 38 41 43 51 52
59 55 32 23 43
Variety 2
18 45 62 59 53 25 13 57
45 41 50 36 62
Answer:
2 | 1 | 3 8
3 0 | 2 | 5
9 8 2 | 3 | 6
3 3 1 | 4 | 1 5 5
9 5 2 1 | 5 | 0 3 7 9
| 6 | 2 2
Step-by-step explanation:
what’s the answer? i really need help ???
Answer:
C, 288 square yards
Step-by-step explanation:
The first step is to find the area of the triangular base. [tex]\frac{6\cdot 8}{2}=24[/tex]. Now you can multiply by the length of the prism, 12, to find the volume. 12*24=288, or option C. Hope this helps!
Joaquin's family is planning to drive from Sandpoint to Grangeville. They have a map on which 1 inch = 62 miles. Joaquin measures the distance on
the map to be almost 4 inches.
If Joaquin's mother drives an average of 50 miles per hour, about how long will their trip take without any stops?
Answer: If you round it, should be about 5 hours.
The actual distance from Sandpoint to Grangeville would be 248 miles. If Joaquin's mother drives an average of 50 miles per hour, the trip will take almost 5 hours without any stops.
Explanation:To solve this problem, we need to calculate the actual distance and then the time it will take. As it is mentioned that 1 inch on the map represents 62 miles in reality, if Joaquin measures the distance on the map to be 4 inches, then the actual distance will be 4 inches * 62 miles per inch = 248 miles. Then, if Joaquin's mother drives at a speed of 50 miles per hour, the time it will take to travel that distance can be calculated by dividing the total distance by the speed. So, 248 miles / 50 mph = 4.96 hours. It means that their trip will take almost 5 hours without any stops.
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Charles owns a hardware store. He put hammers and nails on sale last weekend. His first customer bought 3 hammers and 16 nails for $22.96. His last customer bought 2 hammers and 20 nails for $16.80. What was the sale price for hammers and nails?
Answer: the sale price of one hammer is $6.8
the sale price of one nail is $0.16
Step-by-step explanation:
Let x represent the sale price of one hammer.
Let y represent the sale price of one nail.
His first customer bought 3 hammers and 16 nails for $22.96. It means that
3x + 16y = 22.96- - - - - - - - -1
His last customer bought 2 hammers and 20 nails for $16.80. It means that
2x + 20y = 16.8- - - - - - - - - 2
Multiplying equation 1 by 2 and equation 2 by 3, it becomes
6x + 32y = 45.92
6x + 60y = 50.4
Subtracting, it becomes
- 28y = - 4.48
y = - 4.48/- 28
y = 0.16
Substituting y = 0.16 into equation 2, it becomes
2x + 20 × 0.16 = 16.8
2x + 3.2 = 16.8
2x = 16.8 - 3.2
2x = 13.6
x = 13.6/2
x = 6.8