The school is having a bake sale and the math club is bringing cupcakes. They have 180 total cupcakes, both chocolate and strawberry. The number of chocolate cupcakes is eighteen more than twice the number of strawberry cupcakes. Which system of equations can be used to find the number of chocolate cupcakes, c, and the number of strawberry cupcakes, s? A. c + s = 180 s = 2c - 18 B. c + s = 180 c = 2s + 18 C. c - s = 180 s = 2c + 18 D. c = 2s c - 180 = s

Answers

Answer 1

The correct answer is B) c+s=180, c=2s+18

The number of chocolate and strawberry together make 180. c+s=180.

The number of chocolate is 18 more than twice the number of strawberry; c=2s+18.

Answer 2

Let [tex]s[/tex] be the number of strawberry cupcakes, and [tex]c[/tex] the number of chocolate cupcakes.
From our problem we know that the total number of cupcakes is 180, so [tex]c+s=180[/tex]. We also know that the number of chocolate cupcakes is eighteen more than twice the number of strawberry cupcakes, so [tex]c-18=2s[/tex], or solving for [tex]c[/tex]: [tex]c=2s+18[/tex].
Know we have our system of equations:
[tex] \left \{ {{c+s=180} \atop {c=2s+18}} \right. [/tex]
We can conclude that the correct answer is B. c + s = 180 c = 2s + 18.

Lets solve our equations to find how many cupcakes of each they have:
from our second equation we know that [tex]c=2s+18[/tex]; lets replace that value in our first equation to find the number of strawberry cupcakes:
[tex]2s+18+2=180[/tex]
[tex]3s=162[/tex]
[tex]s= \frac{162}{3} [/tex]
[tex]s=54[/tex]
Now that we know the number of strawberry cupcakes, lets replace that value in our second equation to find the number of chocolate cupcakes:
[tex]c=2(54)+18[/tex]
[tex]c=108+18[/tex]
[tex]c=126[/tex]
As a bonus, we can conclude that the math club have 126 chocolate cupcakes and 54 strawberry cupcakes.

Related Questions

An electronics shop offers a small ic chip for $1.50 per unit and $4.00 for large ic chip. on a certain day, 2200 chips were sold and $5050 is collected. how many small ic chips and how many large ic chips were sold?

Answers

Let s and l represent the numbers of small and large ICs sold that day. The problem statement gives rise to two equations.
.. s + l = 2200
.. 1.50s +4.00l = 5050

Solving these by your favorite method gives
.. s = 1500
.. l = 700

1500 small ICs and 700 large ICs were sold.

To determine the number of small and large IC chips sold, we set up a system of linear equations with the given total number of chips (2200) and total earnings ($5050). Solving the system, we found that 1500 small IC chips and 700 large IC chips were sold.

To solve the problem, we can set up a system of linear equations to represent the sales for small and large IC chips. We have two unknowns: the number of small IC chips (let's call it x) and the number of large IC chips (let's call it y). We have two pieces of information to create our equations:

The total number of chips sold is 2200, so x + y = 2200.

The total amount collected is $5050, so 1.50x + 4.00y = 5050.

Solving this system of equations, we multiply the first equation by 1.50 to align it with the second equation:

1.50x + 1.50y = 3300 (Multiply the first equation)

1.50x + 4.00y = 5050 (Second equation)

Subtracting the first new equation from the second gives us:

2.50y = 1750

Dividing both sides by 2.50 to find y gives us y = 700. That means 700 large IC chips were sold. Now, we can substitute y in the first equation to find x:

x + 700 = 2200

x = 2200 - 700

x = 1500

Hence, 1500 small IC chips and 700 large IC chips were sold.

NEEEDDDDD HELPPPPP ASAPPPPP PLZZZZ!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Hector is training for a race that is 10 kilometers long. On Saturday he ran 2.5 km. He plans to add 0.5 km to his distance every Saturday. Hector's Calculations: 2.5 + 0.5 = 3.0 6.5 + 0.5 = 7.0 3.0 + 0.5 = 3.5 7.0 + 0.5 = 7.5 3.5 + 0.5 = 4.0 7.5 + 0.5 = 8.0 4.0 + 0.5 = 4.5 8.0 + 0.5 = 8.5 4.5 + 0.5 = 5.0 8.5 + 0.5 = 9.0 5.0 + 0.5 = 6.0 9.0 + 0.5 = 9.5 6.0 + 0.5 = 6.5 9.5 + 0.5 = 10.0 The equation equivalent to Hector’s calculations is 2.5 + 0.5x = 10. Use either of these methods to determine how many weeks it will take Hector to reach his goal of a 10 kilometer run.

Answers

Im assuming that all you need to find out is the x variable in "2.5 + 0.5x = 10"
it = 15 so 15 weeks

The number of weeks it will take Hector to reach his goal of a 10-kilometer run will be 15 weeks.

What is a linear equation?

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Hector is training for a race that is 10 kilometers long. On Saturday he ran 2.5 km. He plans to add 0.5 km to his distance every Saturday.

Let 'x' be the number of weeks. Then the equation is given as,

2.5 + 0.5x = 10

0.5x = 7.5

x = 15

The number of weeks it will take Hector to reach his goal of a 10-kilometer run will be 15 weeks.

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Tina’s grandfather put $1000 in the bank for her when she was born. The account has been earning 5.85% interest compounded annually. Tina is now 18 years old. How much money is in the account?

Answers

After 18 years the account has $2,053.00

What information is found in the left column of a two column proof?

Answers

The left column is for statements and the right column is for reasons which justify the corresponding statement.

Answer: C) Statements

A statement is simply a sentence with words and/or math expression. For example, one statement could be "Segment AB is parallel to segment CD". That same statement can be translated to "AB || CD". The two vertical lines indicate "parallel".

Here is the histogram of a data distribution. What is the shape of this distribution?

Answers

This histogram is unimodal skewed. There are two parts to this answer. The first part has to do with the number of modes. This would be the item that is occurring the most frequently. In this case the mode is only 4. It is occurring more than any other.
The second part of this has to do with the distribution of the data as it is displayed on the histogram. There are 4 pieces of data that are only occurimg one time on the right of the histogram. We call this skewing the data. When both sides looks almost the same we say it is symmetric.

tossing a number cube numbered from 1 to 6 and getting an even number that is greater than or equal to 2

Answers

3 because you take away the other numbers and leave the 1, 3 and 5 but I am not in college so.....Good luck

Which is the measure of the reference angle for 227 degrees

Answers

47 degrees

hope this helps<3

Geometrically, the reference angle is the smallest angle between the terminal ray and the x-axis.

Algebraically, the reference angle for X is the smaller of (X mod 180°) and (-X mod 180°).

Here, that would be
.. min(227 mod 180, -227 mod 180)
.. = min(47, 133)
.. = 47 . . . . degrees

_____
"X mod 180" means you subtract the largest multiple of 180 that is smaller than X.
Then 227 mod 180 = 227 -180 = 47
and -227 mod 180 = -227 -(-360) = 133.

What’s a culprit??$$

Answers

not sure maybe a drink look it uo ong my home boys website
Google.com

culprit means the person who is responsible for a crime, or a mess.
hope this helped!
:)

Given that Rectangle MNOP ~ rectangle STUV, what is the length of TU?

Answers

The measure of TU is 15.

We set up a proportion to solve this. Using the similarity statement, we know that MN is proportional to ST, NO is proportional to TU, OP is proportional to UV, and PM is proportional to VS.

NO/TU = OP/UV
10/x = 4/6

Cross multiply to solve it:
10*6 = x*4
60 = 4x

Divide both sides by 4:
60/4 = 4x/4
15=x

Answer:

The measure of TU is 15.

Step-by-step explanation:

Does anyone know how to prove that OAC and OBC are Congruent.

Answers

Hello,

The first step is to see that sides OA, OC, OB are all equal because they are the radii of the circle. Knowing that those sides are equal means that we have isosceles triangles. That gives us that the base angles are the same.

In OAC, we can subtract 118 from 180 to give us 62 degrees for the 2 bases angles. This would make each angle 31 degrees.

In OBC, the base angles are already 31, leaving the other angle 118.

There we have all the angles the same and 2 sides the same.

You could use SAS or ASA to prove that the triangles are congruent.

I hope this helps!
Good luck,
MrEquation

Answer:

You could use SAS or ASA to prove that the triangles are congruent.

Step-by-step explanation:

A company paid $48 for 2 cases of printer paper. Each case contains 12 packages of paper. Next month the company’s office manager needs to order 180 packages of the same paper. If the price per package does not change, what would be the total cost of next month’s order?

Answers

48/24 = $2.00 per package

Trigonometric Help Plz?

Answers

1)

[tex]\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\\\ cos(\theta )=\sqrt{1-sin^2(\theta )}\\\\ -------------------------------\\\\ sin(x)=cos(x)-1\implies sin(x)=\sqrt{1-sin^2(x)}-1[/tex]

[tex]\bf sin(x)+1=\sqrt{1-sin^2(x)}\implies [sin(x)+1]^2=1-sin^2(x) \\\\\\ sin^2(x)+2sin(x)+1=1-sin^2(x)\implies 2sin^2(x)+2sin(x)=0 \\\\\\ 2sin(x)[sin(x)+1]=0\implies \begin{cases} 2sin(x)=0\\ sin(x)=0\\ \measuredangle x=0~,~\pi ~,~2\pi \\ -------\\ sin(x)+1=0\\ sin(x)=-1\\ \measuredangle x=\frac{3\pi }{2} \end{cases}[/tex]

2)

[tex]\bf 3sin(x)+cos^2(x)=2 \\\\\\ 3sin(x)+[1-sin^2(x)]=2 \\\\\\ 3sin(x)-sin^2(x)+1=2 \\\\\\ 3sin(x)-sin^2(x)-1=0 \\\\\\ sin^2(x)-3sin(x)+1=0 \\\\\\ \boxed{[sin(x)-3][sin(x)+1]=0}\impliedby \textit{check closely this }FOIL[/tex]

Matt has $550 in his savings account. He is eager to know how much interest the bank will pay him for the whole year. He knows that the bank pays a 3 percent interest rate. He sits down with a pen, paper, and calculator to find out the simple interest. Let’s help him out. Matt has already jotted down the formula he needs to use: I = P × r × t First, help him substitute the correct values in this formula. Write down the appropriate numbers for principal, rate of interest, and time

Answers

From Matt's formula:
I=P×r×t
P=principle amount (amount invested)
r=rate
t=time
From the information given:
P=$550
r=0.03
t=1
therefore
I=550*0.03*1
I=$16.5

Answer:I = 550 × 0.03 × 1

Step-by-step explanation: from plato

Amanda has a piece of ribbon that is 1/4 yard long. She wants to share ribbon with two friends so they can wear a ribbon for breast cancer awareness month. If each of the 3 friends get the same amount, how much ribbon will each person get?

Answers

They will each get 0.08 yards AKA 2.88 inches AKA 0.28 Feet

Final answer:

To share the ribbon equally among the 3 friends, each person will get 1/12 yard of ribbon.

Explanation:

To determine how much ribbon each person will get, we need to divide the total length of the ribbon equally among all friends.

1/4 yard of ribbon divided by 3 friends gives each person 1/12 yard of ribbon.

Therefore, each person will get 1/12 yard of ribbon for breast cancer awareness month.

What is the sum of 4.2 × 105 and 5.3 × 10^5?

A.)95 × 10^5

B.)95 × 10^10

C.)9.5 × 10^5

D.)9.5 × 10^10

Answers

(4.2*105)+(5.3*10^5)
441 + 530000
530441

-----------

If your problem is (4.2*10^5)+(5.3*10^5), it would be
420000 + 530000
950000

Answer:

Option C.

Step-by-step explanation:

The two expressions are [tex]4.2\times 10^{5}[/tex] and [tex]5.3\times 10^{5}[/tex]

We have to find the total of these two terms.

[tex](4.2\times 10^{5}[/tex] + [tex]5.3\times 10^{5})[/tex]

Now we take out [tex]10^{5}[/tex] as a common term.

[tex]10^{5}(4.2+5.3)[/tex]

= [tex]9.5\times 10^{5}[/tex]

Therefore, Option C. will be the answer.

If two fair dice are rolled, find the probability that the sum of the dice is 77, given that the sum is greater than 33.

Answers

The probability is 3/7

The angle bisector of ∠ACD in rhombus ABCD makes a 64° angle with the diagonal BD . Find the measure of ∠BAD.

Answers

In a rhombus, the diagonals are perpendicular bisectors of each other, meaning they divide each other into two equal parts at a right angle. Let's denote the measure of ∠BAD as x degrees. The measure of ∠BAD is [tex]$ 26^\circ $[/tex].

Since the angle bisector of ∠ACD makes a 64° angle with the diagonal BD, and BD bisects ∠ACD, then ∠ACB = 64° as well. Additionally, since ABCD is a rhombus, opposite angles are equal. Therefore, ∠ABD = ∠ACB = 64°.

Now, considering triangle ABD, we know that the sum of angles in a triangle is 180°. Thus:

[tex]\[ \angle BAD + \angle ABD + \angle ADB = 180^\circ \][/tex]

Substituting the known values:

[tex]\[ x + 64^\circ + 90^\circ = 180^\circ \][/tex]

[tex]\[ x + 154^\circ = 180^\circ \][/tex]

[tex]\[ x = 180^\circ - 154^\circ \][/tex]

[tex]\[ x = 26^\circ \][/tex]

So, the measure of ∠BAD is [tex]$ 26^\circ $[/tex].

To summarize:

1. The angle bisector of ∠ACD in the rhombus makes a 64° angle with diagonal BD.

2. By the properties of a rhombus, ∠ACB = 64° as well.

3. Since opposite angles in a rhombus are equal, ∠ABD = ∠ACB = 64°.

4. In triangle ABD, the sum of angles is 180°.

5. Solving for ∠BAD, we find [tex]$ 26^\circ $.[/tex]

There are approximately 2.2 million births in a country each year. Find the births per minute.

Answers

1. you divide by 365 to get per day,
2. you divide by 24 to get per hour,
3. and then divide by 60 to get per minute.

(1. days in a year, 2. hours in a day, 3. minutes in an hour)

The expression 4i gives the perimeter of a square with a side lengh of i units .
what is the perimeter of a square with a side lenth of 5/7 units ?

Answers

we know that

[perimeter of a square]=4*i

for i=5/7 units
so

[perimeter of a square]=4*(5/7)----------> 20/7 units

the answer is
20/7 units

A worksheet has an area of 48 square inches. Its perimeter is 28 inches. What are the dimensions of the worksheet?

Answers

an area and a perimeter in the same problem means you are working with a 3D shape as such as a rectangular prism

part of the proceeds from a garage sale was $510 worth of $10 and $20 bills. if there were only 6 more $10 bills than $20, find the number for each denomination

Answers

There are 15 $20 bills and 26 $10 bills.

In a region, there is a 0.95 probability chance that a randomly selected person of the population has brown eyes. Assume 13 people are randomly selected. Find the probability that the number of selected people that have brown eyes is 11 or more.

Answers

is there more to this question?

PLEASE HELP!!!!

Which of the following functions is graphed below?!?

Answers

The given graph is for a piecewise function consisting of two intervals:

(1) x ≤ 1 ⇒⇒⇒ the graph in this interval like a cubic function.

(2) x > 1 ⇒⇒⇒ the graph in this interval like a quadratic function

By comparing to the given options

The answer is option c.

Answer:

Option C is correct.

Explanation:

A piece-wise function is a function which is defined by multiple sub-functions, each sub-function applying to a certain interval of the main function's domain.

From the graph we can see that the function is made up of 2 pieces.

Solid dot means- Including

Open-dot means - not- including.

As we can see that the boundary lines are at x=1.

We have to look each line separately to determine each equation:

when [tex]x>1[/tex], it gives the function [tex]y=x^2+4[/tex] and

when [tex]x\leq 1[/tex], it gives the function [tex]y =x^3-2[/tex].

So, the piece-wise function is:

[tex]y=\left \{ {{x^3-2}, x\leq1 \atop {x^2+4}, x>1} \right.[/tex]

The chemical formula for lithium phosphide is Li3P. Which best describes this ionic compound?

Answers

Lithium ions have 1 positive charge, and phosphorus ions have 3 negative charges.

When lithium and phosphorus combine to form lithium phosphide, three lithium cations (Li+) combine with one phosphide anion (P₃-) to balance the charges and form a neutral compound, Li₃P.

What is Ionic compound?

an ionic compound is a chemical compound composed of ions held together by electrostatic forces termed ionic bonding.

The correct description of the ionic compound lithium phosphide, with the chemical formula Li3P, is "Lithium ions have 1 positive charge, and phosphorus ions have 3 negative charges."

This is because lithium is a Group 1A element, which means it has one valence electron that it tends to lose in chemical reactions to form a cation with a charge of +1.

Phosphorus, on the other hand, is a Group 5A element, which means it has five valence electrons and tends to gain three electrons to form an anion with a charge of -3.

Thus, When lithium and phosphorus combine to form lithium phosphide, three lithium cations (Li+) combine with one phosphide anion (P₃-) to balance the charges and form a neutral compound, Li₃P.

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the radius of a quarter circle is 1 mile. What is the quarter circle's perimeter?

Answers

The answer to your question is 6.28mi

Surface area of right cone radius of 8 and 14 height
A. 896
B. 224
C. 176
D. 167

Answers

[tex]\bf \textit{total surface area of a cone}\\\\ S=\pi r\sqrt{h^2+r^2}+\pi r^2\quad \begin{cases} r=radius\\ h=height\\ -----\\ r=8\\ h=14 \end{cases} \\\\\\ S=\pi (8)\sqrt{14^2+8^2}+\pi (8)^2\implies S=8\pi \sqrt{260}+64\pi \\\\\\ S\approx 405.25+201.06\implies S\approx 606.31[/tex]

The value of Surface area of right cone with radius of 8 and 14 height is,

⇒ SA = 606.31

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Radius of cone = 8

And, Height = 14

We know that;

Surface area of right cone is,

SA = πr (r + √h² + r²)

SA = 3.14 × 8 (8 + √14² + 8²)

SA = 606.31

Thus, The value of Surface area of right cone with radius of 8 and 14 height is,

⇒ SA = 606.31

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I need help ASAP!!
What is 92 rounded to the nearest yard??

Answers

Here we will tell you what 92 is rounded to the nearest hundred and also show you what rules we used to get to the answer. First, 92 rounded to the nearest hundred is:

100

Remember, we did not necessarily round up or down, but to the hundred that is nearest to 92.

When rounding to the nearest hundred, like we did with 92 above, we use the following rules:

A) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.

B) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.

C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.

eva estimates that 475 songs will fit on her mp3 player the actual that fit is 380 findc the percent error

Answers

20% is the percent error
https://studysoup.com/questions/math/100256/eva-estimates-the-475-songs-will-fit-on-mp3-player

20 percent is the percent error. Hope I helped! :)

1.
Find the Compound Amount.
Round to the nearest cent.

Amount = $980
Rate = 8%
Compounded = Quarterly
Time (Years) = 5

2.
Find the Interest Earned.
Round to the nearest cent.

Amount = $980
Rate = 8%
Compounded = Quarterly
Time (Years) = 5

Answers

1)
Principal Amount = P = $980
Interest rate = r = 8% = 0.08
Compounding periods = n = 4
Time = t = 5 years

Formula to be used for finding compounding amount:

[tex]A=P (1+ \frac{r}{n} )^{nt} [/tex]

Using the values in the formula, we get:

[tex]A=980 (1+ \frac{0.08}{4} )^{5*4} =1456.23[/tex]

Therefore, the amount compounded over a period of 5 years will be $1456.23

2)
Principal Amount = $980
Compounded Amount = $1456.23
Interest Earned = Compounded Amount - Principal Amount
Interest Earned = 1456.23 - 980 = $ 476.23

Therefore, $476.23 interest will be earned over a period of 5 years.

5 3/4 in a improper fraction?

Answers

5 and 3/4 as an improper fraction would be 23/4. Hope it helps! :)

the improper fraction would be 23/4 because you need to multiply 5 by 4 and get 20 and add 3 which gets you 23. You will keep the denominator so the answer in an improper fraction is 23/4

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