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Carlos divided an amount of $60,000 into three parts, investing them
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04 Sep 2026, 15:34
04 Sep 2026, 15:34
Expert Reply
00:00
Question Stats:
50% (03:14) correct
50% (04:18) wrong based on 2 sessions
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Carlos divided an amount of $60,000 into three parts, investing them at annual interest rates of 3 %, 5 %, and 7 % respectively. The amount invested at 5 % was twice the amount invested at 3 % . The total interest earned from all three parts after one year was $3,200.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
Interest accrued by the part invested at 7% annually |
$ 1,000 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
- Part of the project: GRE Daily Quant Challenge ALL 4 CORE QUANT AREAS
- Also replying to the unanswered questions
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Re: Carlos divided an amount of $60,000 into three parts, investing them
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08 Sep 2026, 09:49
08 Sep 2026, 09:49
1
Expert Reply
Solution
Let the amount invested at 3% be x.
Then the amount at 5% is \(2x,\) so the amount at 7% is:
\(60000-x-2x=60000-3x\)
The total interest is \($3,200:\)
\(0.03x+0.05(2x)+0.07(60000-3x)=3200\)
Simplify:
\(0.03x+0.10x+4200-0.21x=3200,\)
\(4200-0.08x=3200\)
\(0.08x=1000 x=12,500\)
Therefore, the amount invested at 7% is:
\(60000-3(12500)=22,500\)
Interest earned at 7%:
\(0.07(22500)={1575}\)
So:
Quantity A = $1,575
Quantity B = $1,000
Answer: A
Let the amount invested at 3% be x.
Then the amount at 5% is \(2x,\) so the amount at 7% is:
\(60000-x-2x=60000-3x\)
The total interest is \($3,200:\)
\(0.03x+0.05(2x)+0.07(60000-3x)=3200\)
Simplify:
\(0.03x+0.10x+4200-0.21x=3200,\)
\(4200-0.08x=3200\)
\(0.08x=1000 x=12,500\)
Therefore, the amount invested at 7% is:
\(60000-3(12500)=22,500\)
Interest earned at 7%:
\(0.07(22500)={1575}\)
So:
Quantity A = $1,575
Quantity B = $1,000
Answer: A
Re: Carlos divided an amount of $60,000 into three parts, investing them
[#permalink]
08 Sep 2026, 11:09
08 Sep 2026, 11:09
Expert Reply
Elegant solution
