Vincen wrote: ↑

Wed Sep 30, 2020 6:39 am

ACME’s manufacturing costs for sets of horseshoes include an $11,450 initial outlay, and $19.75 per set. They can sell the sets of $52.50. If profit is revenue from sales minus manufacturing costs, and the company produces & sells 987 sets of horseshoes, what was their profit?

(A) $20,874.25
(B) $30,943.25
(C) $41,308.50
(D) $51,817.50
(E) $53,624.25

Answer: A

Solution:

The profit is:

987(52.50) - [11,450 + 987(19.75)]

987(52.50) - 11,450 - 987(19.75)

987(52.50 - 19.75) - 11,450

987(32.75) - 11,450

At this point, we will approximate 987 as 1,000 and 32.75 as 32. So the approximate total profit is:

1,000(32) - 11,450

32,000 - 11,450

20,550

We see that this is closest to 20,874.25 in choice A.

Alternate Solution:

Let’s round all the numbers. From the final statement of the problem, we know we’ll sell about 1,000 sets. The initial outlay is about 12,000 and manufacturing costs are about (20) (1000) = 20,000. Thus, costs are about 32,000. Revenue is a bit greater than (50)(1000) = 50,000. Thus, revenue - cost = 50,000 - 32,000 = 18,000. Thus, profit is a bit greater than $18,000.

Answer: A