3
algebra

A grocer mixes tea worth $6/lb with tea worth $9/lb. How many pounds of the $9 tea should be mixed with 12 pounds of the $6 tea to create a blend worth $7/lb?

A

4 pounds

B

5 pounds

C

6 pounds

D

8 pounds

Correct Answer: C

Choice C is the correct answer. Let xx = pounds of $9 tea.

Equation: 6(12)+9x12+x=7\frac{6(12) + 9x}{12 + x} = 7

Step 1: Multiply both sides by (12+x)(12 + x): 72+9x=7(12+x)72 + 9x = 7(12 + x)72+9x=84+7x72 + 9x = 84 + 7x2x=122x = 12x=6x = 6

Solution: 6 pounds

Verification: 6(12)+9(6)12+6=72+5418=12618=7\frac{6(12) + 9(6)}{12 + 6} = \frac{72 + 54}{18} = \frac{126}{18} = 7

💡 Strategic Tip: Weighted average = total value ÷ total weight.