The numerator of a rational number is greater than its denominator by 5. If the numerator is decreased by 8 and the denominator is increased by 7, the new number obtained is 3/5. Find the number.

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Solution

Let a/b is the fraction,

b+5=a

a-8/b+7=3/5

b+5-8/b+7=3/5

b-3/b+7=3/5

5b-15=3b+21

5b-3b=21+15
2b=36
b=18
a=b+5
a=18+5=23

the fraction is 23/18

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The numerator of a rational number is greater than its denominator by 5. If the numerator is decreased by 8 and the denominator is increased by 7, the new number obtained is 3/5. Find the number.

Let a/b is the fraction, b+5=a a-8/b+7=3/5 b+5-8/b+7=3/5 b-3/b+7=3/5 5b-15=3b+21 5b-3b=21+15 2b=36 b=18 a=b+5 a=18+5=23 the fraction is 23/18

Let a/b is the fraction,

b+5=a

a-8/b+7=3/5

b+5-8/b+7=3/5

b-3/b+7=3/5

5b-15=3b+21

5b-3b=21+15
2b=36
b=18
a=b+5
a=18+5=23

the fraction is 23/18