5

Set 14: Systems of Equations (Advanced)

Explanation

Answer: C

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

✓ Correct
D.

8 pounds

Detailed Explanation

Choice C is correct. Choice C is the correct answer. Let xx = pounds of $9tea. Equation: $$$\frac{6(12) + 9 x}{12 + x} = 7$$ Step 1: Multiply both sides by (12 + x): $$$72+ 9 x = 7(12 + x)$$72+ 9 x = 84 + 7 x$$2x = 12x = 6$$ 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.

Key Steps:

•

The correct answer is 6 pounds

Why others are wrong:
A: Choice A is incorrect and may result from a calculation error.
B: Choice B is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.
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