SAT Math · Systems of two linear equations in two variables · medium

An investor puts a total of 8,000 into two accounts, one earning 4% annual interest and the other earning 7% annual interest. After one…

An investor puts a total of $8,000 into two accounts, one earning 4% annual interest and the other earning 7% annual interest. After one year, the total interest earned is $470. How much more money is in the 7% account than in the 4% account?

Answer and explanation

Answer: A: 2000

Let xx be the amount at 4% and 8000−x8000 - x the amount at 7%. The interest equation is 0.04x+0.07(8000−x)=4700.04x + 0.07(8000 - x) = 470, which simplifies to 560−0.03x=470560 - 0.03x = 470, so 0.03x=900.03x = 90 and x=3000x = 3000. Then the 7% account holds 50005000. The difference is 5000−3000=20005000 - 3000 = 2000, choice A. Check: interest is 120+350=470120 + 350 = 470. Choice B (5000) is the amount in the 7% account, not the difference. Choice C (3000) is the amount in the 4% account. Choice D (1000) has no support. The question asks for how much more, which is a difference.

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