65, 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?

Assume the linear relationship

R = mC + b
where m and b are constants

112 = 85 m + b
238 = 175 m + b
126 = 90m
m = 1.40
b = -7
R = 1.40 C - 7

This is a linear relationship, but it means they will be selling under C < $5 drugs at a loss, or paying people to take them. This is unrealistic.

If R = 185, C = $137.14

A, To find the equation that expresses the retail price R in terms of the cost C, we need to determine the linear relationship between the two variables.

First, we need to find the slope of the line. The slope represents the markup per unit cost. We can calculate the slope using the formula:

slope = (retail price - cost) / (wholesale price - wholesale cost)

For the first drug:

slope = (112 - 85) / (238 - 175) = 27 / 63 ≈ 0.43

For the second drug:

slope = (238 - 175) / (175 - 85) = 63 / 90 ≈ 0.70

Now that we have the slopes, we can use the point-slope form of a linear equation:

R = slope * C + b

where R represents the retail price, C represents the cost, and b represents the y-intercept, which is the retail price when the cost is 0.

For the first drug:

R = 0.43 * C + b₁

For the second drug:

R = 0.70 * C + b₂

B, To find the cost (wholesale price) that a store pays for a drug that retails for $185, we can substitute the retail price R into the equation and solve for C.

Using the equation for the first drug:

185 = 0.43 * C + b₁

Similarly, using the equation for the second drug:

185 = 0.70 * C + b₂

Since we don't have the values of b₁ and b₂, we need more information to calculate the exact cost for each drug.