shadabkhaniet wrote:
A new sales clerk in a department store has been assigned to mark sale items with red tags, and she has marked 30% of the store items for sale. However, 20% of the items that are supposed to be marked with their regular prices are now marked for sale, and 55% of the items that are supposed to be marked for sale are marked with regular prices. What percent of the items that are marked for sale are supposed to be marked with regular prices?
A. 30%
B. 35%
C. 40%
D. 45%
E. 50%
Since this a percent problem, we can assign a “good” number as the total number of items in the store. So, let’s say the total number of items in the store is 100. Since the sales clerk has marked 30% of the store items for sale, she has marked 30 items as sale items, and therefore 70 items are regular-price items.
We assume the total number of items is 100, and let’s assume that x items were supposed to be marked as sales items. Thus, 100 - x items were supposed to be marked as regular-price items.
Looking back at the given information, we know that 20% of the items that are supposed to be marked with their regular prices are now marked for sale, and 55% of the items that are supposed to be marked for sale are marked with regular prices. Thus:
0.2(100 - x) = number of items that are marked as sale items but should be marked as regular-priced items, and thus:
0.8(100 - x) = number of items that are marked (correctly) as regular-price items.
0.55x = number of items that are marked as regular-price items but should be marked as sale items, and thus:
0.45x = number of items that are marked (correctly) as sale items.
Recall that 30 items are marked as sale items and 70 items as regular-price items. Therefore, we have:
0.45x + 0.2(100 - x) = 30
and
0.55x + 0.8(100 - x) = 70
Let’s solve the first equation:
0.45x + 0.2(100 - x) = 30
45x + 20(100 - x) = 3000
45x + 2000 - 20x = 3000
25x = 1000
x = 40
[Note: If we solve the second equation instead of the first, we will also get x = 40.]
The problem asks: “What percent of the items that are marked for sale are supposed to be marked with regular prices?”
Since we have that 0.2(100 - x) is the number of items marked as sale items when they should be marked as regular-price items, and we have that x = 40, there are:
0.2(100 - 40) = .2(60) = 12 such items.
We also have that a total of 30 items are marked for sale, so the percentage of the marked sale items that are supposed to be marked with regular prices is 12/30 = 4/10 = 0.4 = 40%.
Answer: C