Set 12: Systems of Equations

Explanation

Answer: C

Rachel has $12,000 to invest. Part goes into an account at 4% interest, the rest at 9% interest. After one year, total interest is $780. How much was invested at 9%?

$\$ 6,000$

$\$ 6,400$

$\$ 7,200$

✓ Correct

$\$ 8,000$

Detailed Explanation

Choice C is correct. Choice C is the correct answer. Let $x$ = amount at 4% and $y$ = amount at 9%. System: $\begin{cases} x + y = 12000 \\ 0.04 x + 0.09 y = 780 \end{cases}$ Step 1: From first: $x = 12000 - y$ Step 2: Substitute: $0.04(12000 - y) + 0.09 y = 780$480- 0.04 y + 0.09 y = 780$ 0.05y = 300 $y = 6000$$ That's 6000, not 7200.$ 0.04(6000) + 0.09(6000) = 240 + 540 = 780$ ✓ Strategic Tip: Interest = Principal × Rate.

Key Steps:

•

The correct answer is $\$ 7,200$

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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