66, A clothing store sells a shirt clothing $20 for $33 and a jacket costing $60 for $93.
A, If the makeup policy of the store 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 for a suit that retails for $240?
What’s the answer
A clothing store sells a shirt costing $20 for $33 and a jacket costing $60 for $93.
a. If the markup policy of the store 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 for a suit that retails for $240?
A) To find the equation that expresses the retail price R in terms of the cost C (wholesale price), we need to determine the slope (m) and the y-intercept (b) of the linear relationship.
Let's start by finding the slope. The slope can be calculated using the formula:
m = (change in y) / (change in x)
In this case, the change in y is the difference in retail prices, and the change in x is the difference in costs:
m = (33 - 20) / (60 - 20)
m = 13 / 40
Now, let's find the y-intercept (b). This represents the retail price when the cost is zero. We can use one set of data points to solve for b. Let's use the shirt:
20 = (13/40)(60) + b
20 = 78/4 + b
20 = 19.5 + b
b = 20 - 19.5
b = 0.5
Putting it all together, the equation that expresses the retail price R in terms of the cost C is:
R = (13/40)C + 0.5
B) To find out how much the store pays for a suit that retails for $240, we need to solve the equation for C (cost). Rearranging the equation, we have:
C = (40/13)(R - 0.5)
Substituting R = $240 into the equation, we have:
C = (40/13)(240 - 0.5)
C = (40/13)(239.5)
C ≈ 1233.46
Therefore, the store pays approximately $1233.46 for a suit that retails for $240.
A, To express the retail price R in terms of the cost C, we need to determine the slope and y-intercept of the linear equation.
We can start by finding the equation of the line using the two given data points. Let's use the point-slope formula:
Point 1: (cost, retail price) = ($20, $33)
Point 2: (cost, retail price) = ($60, $93)
Slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
m = ($93 - $33) / ($60 - $20)
m = $60 / $40
m = $1.5
Now that we have the slope, we can find the y-intercept (b) using the point-slope formula:
b = y - mx
Taking Point 1:
b = $33 - $1.5 * $20
b = $33 - $30
b = $3
Therefore, the equation expressing the retail price R in terms of the cost C is:
R = 1.5C + 3
B, To find what the store pays for a suit that retails for $240, we need to rearrange the equation to solve for the cost C.
R = 1.5C + 3
Substitute R = $240:
$240 = 1.5C + 3
Now, isolate C:
1.5C = $240 - 3
1.5C = $237
Divide by 1.5 to solve for C:
C ≈ $158
Therefore, the store pays approximately $158 for a suit that retails for $240.