# The cost of 3 lb of grapes is $6.57. what is the constant of proportionality that relates the...

## Question:

The cost of 3 lb of grapes is $6.57. what is the constant of proportionality that relates the cost in dollars y?

## Proportionality Between Variables:

Proportionality explains how two or more variables are related. We say that two variables are proportional if their product or their ratio is equal to a constant (proportionality constant). There are two types of proportionality: direct proportional and inverse proportional. For directly proportional variables, their ratio is equal to the proportionality constant. For inversely proportional variables, their product is equal to the proportionality constant.

## Answer and Explanation:

Let the cost of {eq}x\; \rm lbs {/eq} of grapes be {eq}y {/eq}. Since the total cost increases as the weight of grapes increase, the cost {eq}y {/eq} is directly proportional to the weight {eq}x {/eq} and we can write this as:

- {eq}y\propto x {/eq}

Removing the proportionality sign and adding a proportionality sign, we get:

- {eq}y = kx {/eq}

If the cost of {eq}x = 3\; \rm lb {/eq} of grapes is {eq}y = \$6.57 {/eq}, then:

- {eq}\$6.57 = 3k {/eq}

Solving for *k*, we get:

- {eq}k = \dfrac{\$6.57}{3} {/eq}

- {eq}\boxed{\color{blue}{k = \$2.19}} {/eq}

The proportionality constant is $2.19, which is the cost per lb of grapes.

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from High School Algebra II: Help and Review

Chapter 1 / Lesson 23