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)
  • frei
    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}.

Do you know the answer?
Not sure about the answer?
Find the right answer to the question 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 by subject Pricing, and if there is no answer or no one has given the right answer, then use the search and try to find the answer among similar questions.
Search for other answers
New questions in the category: Pricing
Authorization
*
*

Password generation