At a summertime poolside snack bar, 200 ice cream scoops were sold in one day. Double scoops were sold for $1.25 each and single scoops were sold for $1 each. If the proceeds from the sale of the cones were $221.75, how many of each kinds of cone were sold? In all, how many scoops of ice cream were sold?

Answers

Answer 1

Answer:

a) 87 double scoops and 113 single scoops.

b) 287 scoops of ice cream.


Step-by-step explanation:

1. You need to make a system of equations, where double scoops are represented by [tex]x[/tex] and the single scoops are represented by [tex]y[/tex]:

[tex]\left \{ {{x+y=200} \atop {1.25x+y=221.75}} \right.[/tex]

2. You can apply the Elimination Method:

- Multiply the first equation by -1 to cancel the variable [tex]y[/tex] from the system. Add both equations:

[tex]0.25x=21.75[/tex]

- Solve for [tex]x[/tex]:

[tex]x=\frac{21.75}{0.25}\\x=87[/tex]

- Substitute the value of [tex]x[/tex] into one of the original equations and solve for [tex]y[/tex]:

[tex]87+y=200\\y=113[/tex]

3. You can calculate the total number of scoops of ice cream that where sold as below:

[tex]2x+y[/tex]

4. Substitute values:

[tex]2(87)+113=287[/tex] scoops of ice cream

Answer 2

Answer:  The number of single scoop cones sold is 113, number of double scoop cones is 87 and the total number of cones sold is 287.

Step-by-step explanation:  Given that at a a summertime poolside snack bar, 200 ice cream scoops were sold in one day.

Double scoops were sold for $1.25 each and single scoops were sold for $1 each. The proceeds from the sale of the cones were $221.75.

We are to find the number of single scoop cones, double scoop cones and the number of scoops of ice cream that sold.

We Let x and y represents the number of cones of single scoop and double scoop ice cream that sold.

Then, according to the given information, we have

[tex]x+y=200\\\\\Rightarrow x=200-2y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

and

[tex]1\times x+1.25y=221.75\\\\\Rightarrow x=221.75-1.25y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Comparing equations (i) and (ii), we get

[tex]200-y=221.75-1.25y\\\\\Rightarrow 1.25y-y=221.75-200\\\\\Rightarrow 0.25y=21.75\\\\\Rightarrow y=\dfrac{21.75}{0.25}\\\\\Rightarrow y=87.[/tex]

From equation (i), we get

[tex]x=200-87=113.[/tex]

Therefore, total number of scoops that were sold is

[tex]113+2\times87=113+174=287.[/tex]

Thus, the number of single scoop cones sold is 113, number of double scoop cones is 87 and the total number of cones sold is 287.


Related Questions

A girl's feet are negative 4 over 6 yards from the surface of a pool. A boy's feet are negative 1 over 6 yards from the surface of the pool. Determine whose feet are closer to the surface.

The girl's feet are closer to the surface of the pool because negative 4 over 6 > negative 1 over 6.
The boy's feet are closer to the surface of the pool because negative 4 over 6 < negative 1 over 6.
The girl's feet are closer to the surface of the pool because negative 4 over 6 < negative 1 over 6.
The boy's feet are closer to the surface of the pool because negative 4 over 6 > negative 1 over 6.

Answers

The correct answer is B.

See diagram

EXPLANATION

Let us choose zero to be our reference point. That is zero is representing the surface of the pool.

Since

[tex]-\frac{1}{6}>-\frac{4}{6}[/tex]

Or

[tex]-\frac{4}{6}<-\frac{1}{6}[/tex]

[tex]-\frac{1}{6}[/tex]

will be closer to zero.

We were told that

[tex]-\frac{1}{6}[/tex]

is where the boy's feet are. Therefore his feet are closer to the surface of the pool than the girl's feet.

So the correct answer is

the second option
Final answer:

Given the distances of -4/6 yards (for the girl's feet) and -1/6 yards (for the boy's feet) from the pool's surface, the boy's feet are closer to the pool's surface because -1/6 is greater than -4/6 in the negative number system.

Explanation:

In this problem, we are comparing the positions of the girl's feet and the boy's feet relative to the surface of the pool. We are given that the girl's feet are at a distance of negative 4 over 6 yards from the pool's surface and the boy's feet are at a distance of negative 1 over 6 yards from the pool's surface. The negative numbers here indicate that the feet are below the surface of the pool.

We know that a number closer to zero has a higher value in the negative number system. Therefore, -1/6 is greater than -4/6. So, the boy's feet are closer to the surface of the pool because negative 4 over 6 (the girl's feet) is less than negative 1 over 6 (the boy's feet).

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Use this figure to find each ratio in simplest form.




Answers

We know that

triangles ADE and ABC are similar triangles

so, the ratios of their sides must be same

now, we will find value of sides

we are given

AD=12

DB=6

AE=14

EC=7

[tex]AB=AD+DB[/tex]

now, we can plug values

[tex]AB=12+6[/tex]

[tex]AB=18[/tex]

so, we can get ratio

[tex]\frac{DE}{BC} =\frac{AD}{AB}[/tex]

now, we can plug values

[tex]\frac{DE}{BC} =\frac{12}{18}[/tex]

So, the ratio in simplest form is

[tex]\frac{DE}{BC} =\frac{2}{3}[/tex]..............Answer


the graph of the equation below is a circle. what is the length of the radius of the cirlce? (x+5)2+(y+7)2=21^2

Answers

the radii would equal 7.5

Answer:

21

Step-by-step explanation:

At the end of the equation the 21 is the radius and when squared it becomes the diameter if i am correct

Eighteen oranges are packaged in 3 containers. How many oranges are packaged in 7 containers?

Answers

18/3 = 6

Each container has 6 oranges

6 *7 = 42

Answer: 42 oranges

There are 42 oranges in 7 containers
This is because you ad to divide 18 by 3 which is 6 then you would multiply 7 by 6.

0.38 times 15 1/3 in the simplest form . Explain how you got the answer you got

Answers

You get 1 9/10. You can change 0.38 to 38/100 which simplifies to 19/50. Then u can change 15 1/3 to an improper fraction. You get 46/3. Then multiply 19/50 by 46/3 and you get 19/10 which simplifies to 1 9/10.

Izzy is Iago's little sister. She is counting her coins. Izzy finds that she has three more quarters ($0.25) than she has dimes ($0.10), twice as many nickels ($0.05) as she has dimes, and four times as many pennies ($0.01) as she has dimes. With a total of $7.61 in coins, how many coins of each type does Izzy have?

Answers

Lzzy has three more quarters ($0.25) than she has dimes ($0.10), twice as many nickels ($0.05) as she has dimes, and four times as many pennies ($0.01) as she has dimes.

Let us assume number of dimes = x.

"Three more quarters than dimes" would be = (x+3) quarters .

"Twice as many nickels as dimes " would be = (2x) nickels.

"Four times as many pennies as dimes" would be =(4x) pennies.

Total value of all coins = $7.61.

We can setup an equation now.

0.10*x + 0.25(x+3) + 0.05(2x)+0.01(4x)=7.61.

Let us simplify the equation.

0.10x + 0.25x + 0.75 + 0.10x + 0.04x = 7.61

0.49x + 0.75 = 7.61.

Subtratcing 0.75 from both sides, we get

0.49x = 6.86

Dividing both sides by 0.49, we get

x= 14.

Therefore,

Number of dimes = x = 14.Number of quarters = (x+3) = 14+3 = 17.Number of nickels = 2x = 2*14 = 28.Number of pennies = 4x = 4*14 = 56.

Four car dealers are comparing new car sales. The first dealer sold 18 of the 98 cars on his lot. The second dealer sold 32 of the 120 cars on his lot. The third dealer sold 15 of the 60 cars on his lot, and the fourth dealer sold 46 of the 200 cars on his lot. What is the largest fraction of cars sold on the four lots? A. 23⁄100 B. 1⁄4 C. 9⁄49 D. 4⁄15

Answers

the answer is A. 23/100



if theres a no solution in my equation of:
5x-4=4x+30+x then what do I write ?

Answers

DNE.... does not exist

Remark

There's no ONE solution to this equation. But x can be anything or the solution could be the empty set. Try writing no solution.  If that doesn't work, try empty set [which won't work if you don't know what a set is]. If that doesn't work, write your instructor or if you have notes, see what the notes say.


4. Part A. Find the value of x.
A) x=20
B) x=35
C) x=70
D) x=110

Part B. Find the measure of the unlabeled angle in the previous question.
A) 40°
B) 70°
C) 110°
D) 140°

Answers

Part A: B)35
As the angle y° equals to angle 2x°, y=2x.
And the sum of the angle (x+y+5°)and the angle 2x° is 180°.Therefore,
x+y+5°+2x =180°
x+2x+5°+2x=180°
5x+5° =180°
5x =175°
x =35°


Part B: C)110°
As I said, y =2x
And the unlabled angle eaquals to the angle(x+y+5°).
Therefore,
the unabled angle= x+y+5°
=x+2x+5°
=3x+5°
=3(35°)+5°
=110°

Hey there!!

The measure of the unlabeled angle is ( x + y - 5 ) due to the vertically opposite angles.

We also know 2x = y due to vertically opposite angles

If we add up all the angles, we get 360 degrees.

Hence,  

y + 2x + x + y - 5 + x + y - 5 = 360

4x + 3y - 10 = 360

Add 10 on both sides

4x + 3y = 370

We know 2x = y

Hence,

4x + 3y = 370 can be broken down as ,

4x + y + y + y = 370

4x + 2x + 2x + 2x = 370

10x = 370

x = 370 / 10

x = 37

The unknown angle = x + y - 5

x + 2x - 5

3x - 5

3 ( 37 ) - 5

111 - 5

106

Hence, the unknown angle is 106°

Hope my answer helps!!



Maria's dog weighs 6 times as uch as her rabbit. Together the pets weight 56 pounds. What does Marias dog weigh? How did you figure this out?

Answers

You will have to multiply 56x6=n find out n and that is your answer

The dog weighs 48 pounds

Let r represent the weight of the rabbit

Weight of the dog = 6r

Sum of their weights = 56

6r + r = 56

7r = 56

r = 56/7

r = 8 pounds

The rabbit weighs 8 pounds

The dog weighs :  6 x 8 = 48 pounds

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Tao is making a 7 feet high door. If the height is 1 more than twice its width, what it its width?

Answers

15 ft because double 7 and add 1 more and what dose it make? 15!

-ii 6th grade


Solve 2(x+1)=2x+5

A. All real numbers
B. No solution
C. 0
D. 3

Answers

2(x+1) = 2x+5

2x + 2 = 2x = 5

2 ≠ 5

Answer

B. No solution

B because 2x+2 ≠ 2x+5

I really need help with this

Answers

A line is infinitely long but is only one-dimensional.

A solid is three-dimensional but not infinite.

Geometric space is infinite but is three-dimensional.

So, that leaves a plane, which is two-dimensional and infinitely large. The answer is A plane!

What is the prime factorization of 2x3x5x7

Answers

This is already in prime factored form. If you multiply 2, 3, 5, and 7 you get 2*3*5*7 = 6*35 = 210

So if your book asked "what is the prime factorization of 210?" then the answer would be 2*3*5*7

I'm using the asterisk symbol * in place of x because x is often used as a variable in algebra.

Final answer:

The prime factorization of 2x3x5x7 is simply 2x3x5x7 itself because these are all prime numbers. Prime numbers are numbers that have only two factors: 1 and the number itself. In addition, the product 2x3x5x7 equals to 210, so the prime factorization of 210 is also 2x3x5x7.

Explanation:

The prime factorization of a number is a product of the prime numbers that can multiply together to create the original number. In this case, the product 2x3x5x7 is already a multiplication of prime numbers. Hence, the prime factorization of 2x3x5x7 is simply 2x3x5x7.

Prime numbers are the numbers that have only two factors: 1 and the number itself. Examples of prime numbers are 2, 3, 5, and 7.

On the other hand, the product 2x3x5x7 equals to 210. So the prime factorization of 210 is also 2x3x5x7.

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A cell phone is 9 centimeters long. If the area of the cell phone is 45 square centimeters, what is the width of the cell phone?

Answers

the width is 5 centimeters
5 I believe because if the formula for area it length×width then its 9×?=45. so you would divide 45 by 9 to get your answer. so the answer is 5.

I have a ring for each finger of both hands. I want to buy 4 more rings. How many rings will I have then?

Answers

you will

have 14 rings


you will have 14 rings, because you have ten fingers, and ten plus 4 is 14.

hope it helps.

Please answer quickly thanks :)

In the first drop box it says , "distance from 15.3 to zero on a number line, or opposite of 15.3"
On the second drop box it says , "Negative or positive"

Answers

Positive. The distance from a number to zero is always positive


Positive. The distance from a number to zero is always positive . hope that helps


Evelyn is making a candy that contains 25% dark chocolate and the rest milk chocolate. The candy has 3 pounds of milk chocolate.


Part A: Write an equation using one variable that can be used to find the total number of pounds of dark chocolate and milk chocolate in the candy. Define the variable used in the equation. Hint: 0.25x represents the number of pounds of dark chocolate in the candy. (5 points)


Part B: How many pounds of dark chocolate are present in the candy?

Answers

Part A:

If 25% is dark chocolate and the rest is milk chocolate then, dark + milk = all

25% + milk chocolate= 100%

Subtract 25% from both sides and 100 minus 25 is 75 so, milk chocolate is 75% of all the chocolate.


Now, if there is 3 pounds of milk chocolate then 3 pounds= 75%.

You would divide by 3 so, 75 divided by 3 is 25.

1 pound or lb= 25% which us the amount of dark chocolate that there is.

Now, we know that there milk chocolate is 75% and dark chocolate is 25% of all the chocolate.

M= pounds of milk chocolate

D= dark chocolate

Equation: m divided by d or m/d= 75 divided by 25 or 75/25 or m/d=3 and m=3

3 divided by d or 3/d=3

3=3d

D=1


Part B:

There is 1 pound of dark chocolate in the candy.

Hope this helps! :)

Final answer:

The equation to find the total pounds of dark chocolate and milk chocolate in the candy is 0.25x + 3 = x. There are 4 pounds of dark chocolate present in the candy.

Explanation:

Part A: Let's define the variable x as the total number of pounds of dark chocolate and milk chocolate in the candy. Since the candy contains 25% dark chocolate, we can represent the pounds of dark chocolate as 0.25x. The candy also has 3 pounds of milk chocolate, so we can represent the pounds of milk chocolate as 3. Therefore, the equation is: 0.25x + 3 = x.

Part B: To find the pounds of dark chocolate in the candy, we can solve the equation from Part A. First, subtract 0.25x from both sides: 3 = 0.75x. Then, divide both sides by 0.75 to solve for x: x = 4. Therefore, there are 4 pounds of dark chocolate present in the candy.

Charles has $20 to spend at the bakery he wants to buy six cupcakes and a pie. The pie costs
$12.50.what is the maximum price he can pay for each of the cupcakes?

Answers

the most he can buy for each cupcake is 1.25

How is a table helpful when constructing equations

Answers

Its helpful because it gives you the number to put in and to find the unit rate

Final answer:

Tables aid in constructing equations by facilitating the organization and visualization of mathematical data. This makes it easier to apply given parameters to equations and to understand their behavior. For instance, an equilibrium state can be visually represented in a table.

Explanation:

A table is incredibly helpful when constructing equations because it aids in the organization and visualization of mathematical data. Through the usage of tables, one can clearly list and categorize known values that might be used in an equation, thereby making it easier to identify what needs to be solved. For instance, if you're given multiple variables and constants in a word problem, a table can be used to order these parameters systematically so they can be more easily applied into constructing equations.

Similarly, tables contribute to expressing equations visually as they can illustrate changes in variable values, which can further assist in understanding the behavior of the equation. An equilibrium state, for instance, can be clearly italicized in a table to visually represent the point where an equation balances, which would be harder to see in text form.

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Who is correct and why?

Answers

Armani. 2 x 1.50=3.00
5 x 1.59=7.50

how would you use a number line to round 16800 to the nearest ten thousand?

Answers

Well you'd see if it's closer to 10000 or 20000.

In this case it would round to 20000.

What is the value of x in the equation 1/5 x – 2/3y = 30, when y = 15?

Answers

1/5x - 2/3(15) = 30

Answer is: by simplifying both sides of the equation, then isolating the variable.

x = 200

1/5 x – 2/3y = 30

1/5 x – 2/3 (15) = 30

1/5x - 10 = 30

1/5x = 40

x = 200

23-4x=27
solve for x.

Answers

-4x = 27 - 23
-4x = 4
x = -1

Hello there!

Answer: ⇒ [tex]x=-1[/tex]

_________________________________________________________________

Step-by-step explanation:

First you had to subtract by 23 from both sides of equation.

[tex]23-4x-23=27-23[/tex]

Simplify.

[tex]-4x=4[/tex]

Then you divide by -4 from both sides of equation.

[tex]\frac{-4x}{-4}=\frac{4}{-4}[/tex]

Simplify its should be the correct answer.

[tex]x=-1[/tex]

__________________________________________________________________

Hope this helps!

Thank you for posting your question at here on brainly.

Have a great day!

-Charlie

___________________________________________________________________-

The order pair (5,6) is a solution of a direct variation equation.

Answers

The direct variation equation that is satisfied by this ordered pair is y = 6/5x

In order to find this, we start with the base equation for direct variation. We then plug in and solve for k.

y = kx

6 = k5

6/5 = k

And now we can use that to model all future direct variations with this.

y = 6/5x

0.5-3(0.5+1) with a power of 2

Answers

Answer:   -6.25


Step-by-step explanation: 0.5 -3(0.5+1)^2

                                            =0.5 -3(1.5)^2

                                        =  0.5 -3(2.25)

                                        =  0.5-6.75

                                       =  -6.25


Is in,general, how tall are giraffes? A statistical question or non statistical question

Answers

the height of (my favorite animal if i might add) an adult male giraffe can grow up to 16-20 feet while the females grow up to 15 feet

Answer:

Statistical question.

Step-by-step explanation:

Given question

Is in, how tall are giraffes?

Statistical question is that type of question which have more than one possible answers. The answer of statistical question is the collection of various  points of data. The answer of statistical question depends on variety and situations. The answer of statistical question may be range . Answer of statistical question are more than one.

Non statistical question is that type of question which have only one answer.

For example, the value of 2+2

Answer: 2+2=4

It has only one answer .Therefore , it is non statistical question.

Given question is a statistical question because the height of all giraffes are not same . Height of some giraffes are same and some giraffes have same height. The height  of female giraffes are smaller than the height of male giraffes.

The range of  height of male giraffes lies between 16 feet to 20 feet.

A toll collector on a highway receives $8 for trucks and $3 for sedans. At the end of a 2 hour period, she collected $128. How many trucks and sedans passed through the toll booth during that period?

Answers

There are infinitely many combinations of trucks and sedans that could have passed through the toll booth to collect a total of $128 in 2 hours.

Let's assume the number of trucks that passed through the toll booth in the 2-hour period is represented by 't', and the number of sedans is represented by 's'.

According to the given information, the toll collector received $8 for each truck and $3 for each sedan. We can write two equations based on the total amount collected and solve them simultaneously.

The total amount collected from the trucks:

Amount from trucks = $8 × number of trucks = 8t

The total amount collected from the sedans:

Amount from sedans = $3 × number of sedans = 3s

We are also given that the toll collector collected a total of $128 in 2 hours. So we can write the equation:

Amount from trucks + Amount from sedans = $128

8t + 3s = 128

Now, we need to solve the above two equations simultaneously to find the values of 't' and 's'.

To solve these equations, we can use a method called substitution. Let's solve for 't' in terms of 's' using the first equation:

8t = 128 - 3s

t = (128 - 3s)/8

Now we substitute this value of 't' in the second equation:

8(128 - 3s)/8 + 3s = 128

128 - 3s + 3s = 128

128 = 128

We see that both 's' and 't' have been eliminated from the equation, and we are left with 128 = 128. This means the value of 's' can be any number, as long as it satisfies the equation.

Therefore, there are infinitely many combinations of trucks and sedans that could have passed through the toll booth to collect a total of $128 in 2 hours.

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What is a car loan?

A.
a way to pay in advance for using a car for a given time period
B.
a way to pay for a car that is dependent on the number of miles you drive
C.
a way to borrow money from a bank or financial institution to pay for a car

Answers

C. A way to borrow money from a bank or financial institution to pay for a car

The correct answer is c

i need help solving x^2-2=7 by factoring

Answers

x^2-2=7

Subtract 7 from both sides

x^2-2-7=7-7

x^2-9=0

x^2-3^2=0

Using a^2-b^2=(a+b)(a-b)

Where a=x and b=3

(x-3)(x+3)

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