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Tatiana [17]
2 years ago
15

Owen is making lemonade from concentrate. The number of quarts of water he needs is 4 times the number of quarts of concentrate.

He wants to make 100 quarts of lemonade.
Let c represent the number of quarts of concentrate, and let w represent the number of quarts of water Owen will use. Which of the following systems of equations models this situation?
Mathematics
1 answer:
tiny-mole [99]2 years ago
4 0

Answer:

<u>The system of equation that models the situation is:</u>

<u>w = 4c</u>

<u>w + c = 100</u>

<u>And c = 20 quarts, 4c = 80 quarts and w = 80 quarts.</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the problem correctly:

Owen wants to make 100 quarts of lemonade

Number of quarts of water 4 times the number of quarts of concentrate

2. Which of the following systems of equations models this situation?

c =  number of quarts of concentrate

w = number of quarts of water

Like the alternatives of systems of equations that model the situation were not given, let's write them by ourselves, this way:

w = 4c (Number of quarts of water 4 times the number of quarts of concentrate)

w + c = 100 (Owen wants to make 100 quarts of lemonade)

Now, let's solve for c and w, this way:

w = 100 - c

Substituting w in the first equation, we have:

100 - c = 4c

100 = 5c

c = 20 ⇒ 4c = 20 * 4 = 80

w = 4 * 20

w = 80

<u>The system of equation that models the situation is:</u>

<u>w = 4c</u>

<u>w + c = 100</u>

<u>And c = 20 quarts, 4c = 80 quarts and w = 80 quarts.</u>

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Cloud nine is having a sale on all shirts and pants in the store.Olivia purchased 8 shirts 4 pairs of pants for $176.Raheem purc
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Question is Incomplete; Complete question is given below;

Cloud Nine is having a sale on all shirts and pants in the store. Olivia purchased 8 shirts and 4 pairs of pants for $176. Raheem purchased 3 shirts and 4 pairs of pants for $116. Let x represent the price of a shirt and y represent the price of a pair of pants. Write a system of equations, and use the elimination method to find a reasonable price for a pair of pants.

Answer:

The system of equations are \left \{ {{8x+4y=176} \atop {3x+4y=116}} \right.

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Step-by-step explanation:

Let the price of shirt be 'x'.

Let price of pair of pants be 'y'.

Given:

Olivia purchased 8 shirts 4 pairs of pants for $176

So we can say that;

8 multiplied by the price of shirt plus 4 multiplied by the price of pair of  pants is equal to 176.

framing in equation form we get;

8x+4y=176 \ \ \ \ equation \ 1

Also Given:

Raheem purchased 3 shirts and 4 pairs of pants for 116.

So we can say that;

3 multiplied by the price of shirt plus 4 multiplied by the price of pair of pants is equal to 116.

framing in equation form we get;

3x+4y=116 \ \ \ \ equation \ 2

Hence the system of equation are \left \{ {{8x+4y=176} \atop {3x+4y=116}} \right.

Now by using elimination method we will subtract equation 2 from equation 1 we get;

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Now Substituting the value of x in equation 1 we get;

8x+4y=176\\\\8\times 12+4y =176\\\\96+4y=176\\\\4y =176-96\\\\4y = 80\\\\y= \frac{80}{4} =\$ 20

Hence The reasonable price for pair of pants is $20.

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