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%

The Picking Numbers strategy would be ideal for this problem, since there are percentages without given values. Let's use 100 as the total number of items in the store. This means that 30 of the items are marked for sale and 70 are marked at regular price. We are also told that 20% of the regular-priced items are marked for sale, and 55% of the sale items are marked at regular price. This means that 45% of the sale items are marked for sale. We can set up an equation with x as the number of regular-priced items and y as the number of sale items: 0.2x + 0.45y = 30.

Since 20% of the regular-priced items are marked incorrectly and 45% of the sale items are marked correctly, 80% of the regular-priced items are marked at regular price and 55% of the sale items are marked at regular price. This information gives us the next equation: 0.8x + 0.55y = 70.

Combining these 2 equations, we have a system of equations that we can solve. Multiply both sides of the equation 0.2x + 0.45y = 30 by –4 so that we can subtract it from 0.8x + 0.55y = 70 and isolate the y variable.

Now we know that the number of sale items is 40, so the number of regular-priced items must be 100 – 40 = 60. We can now calculate the number of regular-priced items marked for sale: Since 20% of 60 is 12 and the total number of items marked for sale is 30, the percent would be .

So, 40% of the items marked for sale are supposed to be marked at regular price.

Answer Choice (C) is correct.

Confirm Your Answer:

Plug the numbers we figured back into the problem. Out of the 30 items marked for sale, 12 are marked incorrectly, so 30 – 12 = 18 of the sale items are actually on sale. Eighteen is indeed 45% of 40, so the correct number of sale items is 40. Our answer is confirmed.