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A clothing store sells a shirt costing {eq}$20 {/eq} for {eq}$33 {/eq} and a jacket costing {eq}$60 {/eq} for {eq}$93 {/eq}. If the markup policy of the store is assumed to be linear, write an equation that expresses retail price {eq}R {/eq} in terms of cost {eq}C {/eq} (wholesale price). What does a store pay for a suit that retails for {eq}$240 {/eq}?

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The markup policy of the store is assumed to be linear, meaning that the retail price is a linear function of the cost. Let's assume that the markup rate is {eq}m {/eq} (the markup rate is the percentage of markup as a fraction of the cost) and the fixed cost is {eq}b {/eq} (the fixed cost is the amount added to the markup to get the retail price).

Then the equation for the retail price {eq}R {/eq} in terms of cost {eq}C {/eq} is:

{eq}R = mC + b {/eq}

We can find the values of {eq}m {/eq} and {eq}b {/eq} using the given information.

For the shirt, the markup is {eq}$33 - $20 = $13 {/eq} and the cost is {eq}$20 {/eq}, so:

{eq}13 = m(20) + b {/eq}

For the jacket, the markup is {eq}$93 - $60 = $33 {/eq} and the cost is {eq}$60 {/eq}, so:

{eq}33 = m(60) + b {/eq}

We now have two equations with two unknowns, {eq}m {/eq} and {eq}b {/eq}. Solving for {eq}m {/eq} and {eq}b {/eq}, we get:

{eq}m = \frac{13 - 33}{20 - 60} = 0.5 {/eq}

{eq}b = 13 - (0.5)(20) = 3 {/eq}

So the equation for the retail price {eq}R {/eq} in terms of cost {eq}C {/eq} is:

{eq}R = 0.5C + 3 {/eq}

To find what the store pays for a suit that retails for {eq}$240 {/eq}, we can rearrange the equation to solve for the cost {eq}C {/eq}:

{eq}C = \frac{R - b}{m} {/eq}

Substituting {eq}R = $240 {/eq}, {eq}m = 0.5 {/eq}, and {eq}b = 3 {/eq}, we get:

{eq}C = \frac{240 - 3}{0.5} = $474 {/eq}

Therefore, the store pays {eq}$474 {/eq} for a suit that retails for {eq}$240 {/eq}.