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The sum of two positive numbers is 5 times their difference. What is the ratio of the larger number to the smaller number?

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I need help with this question.

Guest Sep 8, 2017
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#1
+26470
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Let the numbers be n and m, with n > m

n + m = 5(n - m)

Distribute the 5 on the right

n + m = 5n - 5m

n + 6m = 5n

Subtract n from both sides

6m = 4n

Divide both sides by 4

1.5m = n

Divide both sides by m

1.5 = n/m

or n/m = 1.5.    This is the ratio of the larger number to the smaller.

Alan  Sep 8, 2017
#2
+1

Thank you for the answer! I have a question: Why should we divide it by 4 first instead of 6?

Guest Sep 8, 2017
#3
+26470
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Because it is n/m that you want to get on its own (ie the larger number divided by the smaller one), so you want to get n on its own first.

Alan  Sep 8, 2017

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