19.03.2023 - 09:07

# A clothing store sells a shirt costing $20 for$33 and a jacket costing $60 for$93. If the markup policy of the store is assumed to be linear, write an equation that expresses retail price R in terms

Question:

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}? Answers (1) • April 6, 2023 в 20:40 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}.

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