10
algebra

David has $8,000 to invest. He puts part in stocks earning 8% annually and the rest in bonds earning 5% annually. After one year, his total interest is $550. How much did he invest in stocks?

A

\3,000$

B

\3,500$

C

\4,000$

D

\5,000$

Correct Answer: D

Choice D is the correct answer. Let ss = amount in stocks and bb = amount in bonds.

System: {s+b=80000.08s+0.05b=550\begin{cases} s + b = 8000 \\ 0.08s + 0.05b = 550 \end{cases}

Step 1: From first: b=8000−sb = 8000 - s

Step 2: Substitute: 0.08s+0.05(8000−s)=5500.08s + 0.05(8000 - s) = 5500.08s+400−0.05s=5500.08s + 400 - 0.05s = 5500.03s=1500.03s = 150s=5000s = 5000

Solution: $5,000 in stocks (and $3,000 in bonds)

Verification: 0.08(5000)+0.05(3000)=400+150=5500.08(5000) + 0.05(3000) = 400 + 150 = 550 ✓

💡 Strategic Tip: Investment interest = principal × rate.

Choice A is incorrect because 0.08(3000)+0.05(5000)=240+250=490 eq5500.08(3000) + 0.05(5000) = 240 + 250 = 490 \ eq 550.

Choice B is incorrect because 0.08(3500)+0.05(4500)=280+225=505 eq5500.08(3500) + 0.05(4500) = 280 + 225 = 505 \ eq 550.

Choice C is incorrect because 0.08(4000)+0.05(4000)=320+200=520 eq5500.08(4000) + 0.05(4000) = 320 + 200 = 520 \ eq 550.

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Linear Functions Set 57