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A recipe calls for of a cup of milk for 11 cookies. How many cups of milk are needed to make 132...

Question:

A recipe calls for of a cup of milk for 11 cookies.

How many cups of milk are needed to make 132 cookies?

Proportions in Math:

In mathematics, a proportion is an equation that indicates that two ratios, represented as fractions, are equal. That is, if the ratios, a:b and c: d, are equivalent, then the proportion indicating that would be {eq}\frac{a}{b}=\frac{c}{d} {/eq}. We can use proportions to solve many different applications in mathematics.

Answer and Explanation:

In the scenario described, we would need 12 cups of milk to make 132 cookies.

We are given that a recipe calls for 1 cup of milk for 11 cookies. This can be represented with the ratio of cookies to milk as 11:1. If we let x be the number of cups of milk that would be needed to make 132 cookies, then we would have an equivalent ratio of 132:x. That is, 11 cookies is to 1 cup of milk as 132 cookies is to x cups of milk. This gives the proportion {eq}\frac{11}{1}=\frac{132}{x} {/eq}, and we can solve this proportion for x to find the number of cups of milk needed to make 132 cookies.

  • {eq}\frac{11}{1}=\frac{132}{x} {/eq}

Multiply both sides of the equation by x, and simplify.

  • 11x = 132

Divide both sides of the equation by 11.

  • x = 12

We get that x = 12, so we would need 12 cups of milk to make 132 cookies.


Learn more about this topic:

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What is a Proportion in Math? - Definition & Practice Problems

from High School Algebra I: Help and Review

Chapter 23 / Lesson 15
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