10
algebra

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%?

A

\5,000$

B

\5,500$

C

\6,000$

D

\6,500$

Correct Answer: C

Choice C is the correct answer. Let xx = amount at 3% and yy = amount at 7%.

System: {x+y=100000.03x+0.07y=540\begin{cases} x + y = 10000 \\ 0.03x + 0.07y = 540 \end{cases}

Step 1: From first: x=10000−yx = 10000 - y

Step 2: Substitute: 0.03(10000−y)+0.07y=5400.03(10000 - y) + 0.07y = 540300−0.03y+0.07y=540300 - 0.03y + 0.07y = 5400.04y=2400.04y = 240y=6000y = 6000

Solution: $6,000 at 7%

Verification: 0.03(4000)+0.07(6000)=120+420=5400.03(4000) + 0.07(6000) = 120 + 420 = 540 ✓

💡 Strategic Tip: Interest = Principal × Rate × Time.

**Other choices fail verification.

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Linear Functions Set 58