10

Set 9: Linear Equations

Explanation

Answer: B

You have $1000 to invest. Part at 5% interest and part at 8%. If the total interest is $68, how much was invested at 8%?

A.

500

B.

600

✓ Correct
C.

800

D.

400

Detailed Explanation

Choice B is correct. Choice A is the correct answer. 1. Define: 8% = xx, 5% = 1000−x1000- x. 2. Equation: 0.08x+0.05(1000−x)=680.08x + 0.05(1000 - x) = 68 3. Simplify: 0.08x+50−0.05x=680.08x + 50 - 0.05 x = 68 4. Combine: 0.03x=180.03x = 18 5. Divide by 0.03: x=600x = 600 6. Verify: 0.08(600)+0.05(400)=48+20=680.08(600) + 0.05(400) = 48 + 20 = 68 ✓ Choice D is incorrect because this is the amount at 5%. Choice C is incorrect because it results from an error in the solution process. Choice B is incorrect because it results from an error in the solution process.

Key Steps:

•

The correct answer is 600

Why others are wrong:
A: Choice A is incorrect and may result from a calculation error.
C: Choice C 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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