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?

a. R = (112/85)C,

R = 1.32C.

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

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

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.

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

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

Thanks, MathMate!

A, Sure thing! Let's find the equation for the linear markup policy.

First, let's find the slope (m) of the line. The slope represents the markup per dollar of cost, which is the increase in retail price for every dollar increase in wholesale price.

For the first drug, the cost (C1) is $85 and the retail price (R1) is $112. The slope is calculated as (R1 - C1) / (C1) = (112 - 85) / 85.

So, for the first drug, the slope (m1) is (112 - 85) / 85.

For the second drug, the cost (C2) is $175 and the retail price (R2) is $238. The slope is calculated as (R2 - C2) / (C2) = (238 - 175) / 175.

So, for the second drug, the slope (m2) is (238 - 175) / 175.

Now, let's find the average slope (m_avg). We can calculate it by taking the average of the two slopes: m_avg = (m1 + m2) / 2.

Once we have the average slope (m_avg), we can find the equation for the linear markup policy: R = C + m_avg * C.

B, Now let's find out what a store pays for a drug that retails for $185.

Using the equation from part A, we need to solve for C, the cost of the drug.

185 = C + m_avg * C

Let's plug in the average slope (m_avg) we calculated earlier and solve for C:

185 = C + (m_avg) * C

Simplifying, we get:

185 = C(1 + m_avg)

Dividing both sides by (1 + m_avg), we find:

C = 185 / (1 + m_avg)

Using the calculated average slope (m_avg) and rounding to the nearest dollar, the store would pay approximately $145 for a drug that retails for $185.

A. To find the equation that expresses the retail price (R) in terms of the cost (C), we can use the information provided in the problem.

Let's consider the data we have:
- For a drug costing $85, it is being sold for $112.
- For a drug costing $175, it is being sold for $238.

We can assume that the markup policy of the drugstore linearly increases the cost to get the retail price. So, we can write the equation in the form: R = mC + b, where 'm' represents the markup rate and 'b' represents the base retail price.

To find the values of 'm' and 'b', we can use the given data points. Let's use the first data point (85, 112):

112 = m * 85 + b

Next, we can use the second data point (175, 238):

238 = m * 175 + b

Now we have a system of two linear equations:
112 = m * 85 + b
238 = m * 175 + b

We can solve this system of equations using any method (substitution, elimination, or matrices) to find the values of 'm' and 'b'.

B. Now, to find the cost (to the nearest dollar) for a drug that retails for $185, we can substitute the given retail price value (R = 185) into the equation we obtained in part A.

R = mC + b

185 = m * C + b

We know that 'b' is the base retail price, which we found when solving the system of equations in part A. So, we substitute the value of 'b' and rearrange the equation:

185 = m * C + (value of 'b' obtained from part A)

Now, we can solve this equation for 'C' to find the cost to the nearest dollar for a drug that retails for $185.