3
algebra

A coffee blend is made by mixing Brazilian beans at $8/lb with Colombian beans at $12/lb. How many pounds of Colombian beans should be mixed with 15 pounds of Brazilian beans to make a blend worth $10/lb?

A

12 pounds

B

15 pounds

C

18 pounds

D

20 pounds

Correct Answer: B

Choice B is the correct answer. Let cc = pounds of Colombian beans.

Equation: 8(15)+12c15+c=10\frac{8(15) + 12c}{15 + c} = 10

Step 1: Multiply both sides by (15+c)(15 + c): 120+12c=10(15+c)120 + 12c = 10(15 + c)120+12c=150+10c120 + 12c = 150 + 10c2c=302c = 30c=15c = 15

Solution: 15 pounds of Colombian beans

Verification: 8(15)+12(15)15+15=120+18030=30030=10\frac{8(15) + 12(15)}{15 + 15} = \frac{120 + 180}{30} = \frac{300}{30} = 10

💡 Strategic Tip: Average price = total value ÷ total weight.

**Other choices fail verification.