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The ratio of two numbers is 7/6. If the smaller of the two numbers is decreased by two the ratio is 7/5, what is the larger number?
A. 28
B. 21
C. 14
D. 12
E. 10
A. 28
B. 21
C. 14
D. 12
E. 10
25 Dec 2017, 01:49
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Bunuel
The ratio of two numbers is 7/6. If the smaller of the two numbers is decreased by two the ratio is 7/5, what is the larger number?
A. 28
B. 21
C. 14
D. 12
E. 10
A. 28
B. 21
C. 14
D. 12
E. 10
Questions which change an old to a new ratio can often be tricky so we'll use the answers.
This is an Alternative approach.
We'll start with the median answer - 14.
If the larger number is 14 the smaller is 14* (6/7) = 12.
If this is decreased by 2 to 10 then the new ratio is 14/10 = 7/5.
Yes!
(C) is our answer.
* Had (C) not been correct we would have gone up to (B) or down to (D) depending on if we needed to increase or decrease our answer.
25 Dec 2017, 12:01
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Bunuel
The ratio of two numbers is 7/6. If the smaller of the two numbers is decreased by two the ratio is 7/5, what is the larger number?
A. 28
B. 21
C. 14
D. 12
E. 10
1) Set up the original ratio with a multiplier, xA. 28
B. 21
C. 14
D. 12
E. 10
The ratio of two numbers is 7/6 : \(\frac{7x}{6x}\)
2) Set up the equation*
The smaller number is decreased by two (LHS):
\(\frac{7x}{6x-2}\)
The new ratio is \(\frac{7}{5}\) (RHS), so
\(\frac{7x}{6x-2} = \frac{7}{5}\)
\(5(7x) = 7(6x - 2)\)
\(35x = 42x - 14\)
\(14 = 7x\)
\(x = 2\)
That multiplier, x, is only for original ratio, \(\frac{7x}{6x}\)
3) Larger number's value? x = 2
Larger number = 7x = (7)(2) = 14
Answer C
*the number added to 6x and the numbers in the new ratio are just numbers, i.e., not accompanied by any multiplier x
