Question

A drugstore sells a drug costing $85 for $112 and drug costing $175 for $238.
A, If the markup policy of the drugstore is assumed to be linear, write an equation that expresses retail price R in terms of cost C (wholesale price).
B, what does a store pay (to the nearest dollar) for a drug that retails for $185?

Answer 1

A.) Cost 85, Retail 112
Cost 175, Retail 238

For the equation
(x,R), x = cost
(85,112), (175,238)

Since linear, use y = mx + b
R = mx + b
slope m = 238 - 112/(175 - 85)
slope m = 126/90 = 1.4

R = 1.4x + b
To find b, plug in (85,112)
112 = 1.4(85) + b
112 = 119 + b
b = -7

R = 1.4x - 7

B. R = 1.4x - 7
185 = 1.4x - 7
192 = 1.4x
x = 137

I am not a tutor, so I am not 100% sure this is how this is done.

But if you check the orig. given info if seems to work.

R = 1.4 x - 7
x = cost, R = retail
(x,R) = (85,112)
112 = 1.4(85) - 7
112 = 119 - 7
112 = 112

(x,R) = (175,238)
238 = 1.4(175) - 7
238 = 245 - 7
238 = 238

Answer 2

a. R = (112/85)C,
R = 1.32C.

b. R = 1.32C,
C = R/1.32 = 185 / 1.32 = 140.

Answer 3

I favour helper's approach.

The question states that the markup is linear, but did not say it passes through the origin. That explains why the ratios 112/85 and 238/175 are different.

According to helper, the markup is 40% less 7$, which works for both given cases.

So for a retail price of 185, the wholesale price is (185+7)/1.4 = $137.14.

The only doubt is the negative value -$7, which causes a problem for items where the wholesale price is below 17.5$.

At wholesale = 17.5, retail equals wholesale! Below that price, items are sold at a loss.

Answer 4

Since, the problem states to use R and C for the equation, change the x to C.

So, the equation would be,
R = 1.4C - 7

Instead of,
R = 1.4x - 7

Answer 5

Yes, I noticed the difference in he ratios; but I assumed the 238 was probably meant to be 231.

Thanks, MathMate!