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The combined salaries of three brothers is $90,000. Mr. Big
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30 Apr 2019, 01:06
30 Apr 2019, 01:06
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The combined salaries of three brothers is $90,000. Mr. Big earns twice what Mr. Small earns, and Mr. Middle earns \(1 \frac{1}{2}\) times what Mr. Small earns. What is the smallest salary of the three brothers?
(A) 20,000
(B) 22,000
(C) 25,000
(D) 30,000
(E) 40,000
(A) 20,000
(B) 22,000
(C) 25,000
(D) 30,000
(E) 40,000
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Re: The combined salaries of three brothers is $90,000. Mr. Big
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20 Apr 2020, 16:18
20 Apr 2020, 16:18
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Carcass wrote:
The combined salaries of three brothers is $90,000. Mr. Big earns twice what Mr. Small earns, and Mr. Middle earns \(1 \frac{1}{2}\) times what Mr. Small earns. What is the smallest salary of the three brothers?
(A) 20,000
(B) 22,000
(C) 25,000
(D) 30,000
(E) 40,000
(A) 20,000
(B) 22,000
(C) 25,000
(D) 30,000
(E) 40,000
B = 2S and M = 1.5S
=> B + M + S = 2S + 1.5S + S = 4.5S
=> 4.5S = 90000
=> S = 20000
Answer A
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Re: The combined salaries of three brothers is $90,000. Mr. Big
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08 Jun 2020, 18:45
08 Jun 2020, 18:45
1
Expert Reply
Carcass wrote:
The combined salaries of three brothers is $90,000. Mr. Big earns twice what Mr. Small earns, and Mr. Middle earns \(1 \frac{1}{2}\) times what Mr. Small earns. What is the smallest salary of the three brothers?
(A) 20,000
(B) 22,000
(C) 25,000
(D) 30,000
(E) 40,000
(A) 20,000
(B) 22,000
(C) 25,000
(D) 30,000
(E) 40,000
This is a straightforward problem to solve either algebraically or by backsolving. Backsolving is particularly useful here, since the numbers are
easy to work with, and the math isn't complicated.
Since we're looking for the smallest salary, start with (A): $20,000
If the smallest salary is 20,000, then the largest salary is twice that, or 40,000. The total of small + large is 60,000, meaning that the remaining person's salary would be 30,000. Since 30,000 is \(1\)\frac{1}{2} 20,000, we have our answer!
If you'd prefer to use algebra, call the smallest salary "s".
So: \(s+1.5s+2s=90,000\)
\(4.5s=90,000\)
\(s=20,000\)
Answer: A
