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Question

A credit card promotion offers a discount on all purchases made with the card. The discount is directly proportional to the size of the purchase. If you save $1.35 on a$20 purchase, how much will you save on a $173 purchase?

Solution

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Step 1
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The variation equation is

d=ksd=ks

where kk represents the constant of variation, dd is the discount and ss the size of the purchase.

First, find the constant of variation.

To find the constant of variation, substitute in the variation equation 1.351.35 for dd and 2020 for ss.

1.35=k20Divide both sides by 20.1.3520=kk=0.0675\begin{align*} 1.35&=k\cdot20&&\text{Divide both sides by $20$.}\\ \dfrac{1.35}{20}&=k\\ k&=0.0675 \end{align*}

The constant of variation is 0.06750.0675.

Now, substitute in the variation equation 173173 for ss and 0.06750.0675 for kk to find dd.

d=0.0675173d=11.6775\begin{align*} d&=0.0675\cdot173\\ d&=11.6775 \end{align*}

You will save $11.6775\$11.6775 on a $173\$173 purchase.

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