# SAT Math Multiple Choice Question 746: Answer and Explanation

### Test Information

Question: 746

11. Perfectioner's Chocolate Company makes two varieties of truffles: dark chocolate and milk chocolate. Each dark chocolate truffle requires 0.65 ounces of cocoa powder, and each milk chocolate truffle requires 0.45 ounces of cocoa powder. If cocoa powder costs c dollars per pound, and Perfectioner's Chocolate Company has budgeted \$200 per week for cocoa powder, which of the following inequalities indicates the restrictions on the number of dark chocolate truffles, d, and the number of milk chocolate truffles, m, the company can make in one week? (1 pound = 16 ounces)

• A.
• B.
• C.
• D.

Explanation:

C

Problem Solving (rates) HARD

This question asks us to write a mathematical statement that "indicates the restrictions" in this situation. So, what keeps us from making as many truffles as we want? Simple: we are only allowed to spend \$200 per week on cocoa powder. Therefore, we can state the restriction on truffles as "the total cost of cocoa powder for our weekly production of truffles must be less than or equal to \$200."

Now we must figure out a way to express "the total cost of cocoa powder for our weekly production of truffles." Clearly, this is the total cost for the dark chocolate truffles plus the total cost for the milk chocolate truffles:

Cost of cocoa powder for d dark chocolate truffles:

Simplify:

Cost of cocoa powder for m milk chocolate truffles:

Simplify:

The total cost for cocoa powder must not be greater than \$200:

Multiply by 16:

3,200 ≥ 0.65cd + 0.45cm

Divide by c: