10
algebra

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%?

A

\6,000$

B

\6,400$

C

\7,200$

D

\8,000$

Correct Answer: C

Choice C is the correct answer. Let xx = amount at 4% and yy = amount at 9%.

System: {x+y=120000.04x+0.09y=780\begin{cases} x + y = 12000 \\ 0.04x + 0.09y = 780 \end{cases}

Step 1: From first: x=12000−yx = 12000 - y

Step 2: Substitute: 0.04(12000−y)+0.09y=7800.04(12000 - y) + 0.09y = 780480−0.04y+0.09y=780480 - 0.04y + 0.09y = 7800.05y=3000.05y = 300y=6000y = 6000

That's 6000, not 7200. 0.04(6000)+0.09(6000)=240+540=7800.04(6000) + 0.09(6000) = 240 + 540 = 780 ✓

💡 Strategic Tip: Interest = Principal × Rate.

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Linear Functions Set 59