Set 7: Systems of Equations (Advanced)

Explanation

Answer: C

Maria invests $10,000 split between two accounts. One earns 3% annually, the other 7% annually. After one year, total interest is $540. How much was invested at 7%?

$\$ 5,000$

$\$ 5,500$

$\$ 6,000$

✓ Correct

$\$ 6,500$

Detailed Explanation

Choice C is correct. Choice C is the correct answer. Let $x$ = amount at 3% and $y$ = amount at 7%. System: $\begin{cases} x + y = 10000 \\ 0.03 x + 0.07 y = 540 \end{cases}$ Step 1: From first: $x = 10000 - y$ Step 2: Substitute: $0.03(10000 - y) + 0.07 y = 540$300- 0.03 y + 0.07 y = 540$ 0.04y = 240 $y = 6000$$ Solution: \$ 6,000 at 7% Verification: $0.03(4000) + 0.07(6000) = 120 + 420 = 540$ ✓ Strategic Tip: Interest = Principal × Rate × Time. Other choices fail verification.

Key Steps:

•

The correct answer is $\$ 6,000$

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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