In the sharpeners problem, which option gives the cost of the white sharpener and how many were bought?

• A. 5, 13
• B. 5, 10
• C. 6, 10
• D. None of these

Answer: (C)

The idea being tested is turning a word problem with two types of items into a simple two-equation system, then solving for the two unknowns: how many white sharpeners were bought and what their price is. You treat white sharpeners as one group and the other color as the second group. Let x be the number of white sharpeners bought, and w the cost of one white sharpener. Let y be the number of the other color sharpeners and r their cost. The problem gives two totals: the total number of sharpeners and the total money spent. From that you write two equations: x + y equals the total number bought, and w x + r y equals the total cost. Substituting y = total minus x into the cost equation gives (w − r) x = total cost − r times the total, so you can solve for x. Once you have x, you can plug back in to find w, confirming the cost of the white sharpener. When the data are worked through, the numbers that satisfy both equations are that the white sharpener costs 6 and 10 white sharpeners were bought. This pair makes both the count and the total cost come out correctly, whereas other candidate pairs would break one of the totals.