Question

What must be added to each term of the ratio 2:5 so that it maay be equal to 5:6

Answer 1

9514 1404 393

Answer:

  13

Step-by-step explanation:

Let n represent that number.

  (2 +n)/(5 +n) = 5/6 . . . . . . . . n is added to numerator and denominator

  6(2 +n) = 5(5 +n) . . . . . . . . . multiply by 5(5+n)

  12 +6n = 25 +5n . . . . . . . . . eliminate parentheses

  n = 13 . . . . . . . . . . . subtract 5n+12

Adding 13 to each term will give 5/6.

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Check

  (2 +13)/(5 +13) = 15/18 = (3·5)/(3·6) = 5/6

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Alternate solution

The difference of denominator and numerator in 2/5 is 5-2 = 3. The difference of denominator and numerator in 5/6 is 6-5 = 1. In order to make the latter difference 3, we must have (3/3)(5/6) = 15/18. We can get 15/18 from 2/5 by adding 13 to numerator and denominator.