Find a fraction which reduces to 3 by 4 when both the numerator and denominator are each decreased by 1 and reduces to 5 by 6 when both the numerator and denominator are each increased by 3

Answer 1

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Answer 2

Hello , does anybody know the answer

Answer 3

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Answer 4

n = numerator

d = deniminator

reduces to 3 by 4 when both the numerator and denominator are each decreased by 1 means:

( n - 1 ) / ( d - 1 ) = 3 / 4

Cross multiply

4 ( n - 1 ) = 3 ( d - 1 )

4 n - 4 = 3 d - 3

Add 4 to both sides

4 n = 3 d + 1

Divide both sides by 4

n = ( 3 d + 1 ) / 4

reduces to 5 by 6 when both the numerator and denominator are each increased by 3 means:

( n + 3 ) / ( d + 3 ) = 5 / 6

Cross multiply

6 ( n + 3 ) = 5 ( d + 3 )

6 n + 18 = 5 d + 15

Subtract 18 to both sides

6 n = 5 d - 3

Divide both sides by 6

n = ( 5 d - 3 ) / 6

n in first equation us equal n in second equation.

n = n

( 3 d + 1 ) / 4 = ( 5 d - 3 ) / 6

Cross multiply

6 ( 3 d + 1 ) = 4 ( 5 d - 3 )

18 d + 6 = 20 d - 12

Subtract 18 d to both sides

6 = 2 d - 12

Add 12 to bith sides

18 = 2 d

2 d = 18

d = 18 / 2

d = 9

Put this value in equation:

n = ( 3 d + 1 ) / 4

n = ( 3 • 9 + 1 ) / 4

n = ( 27 + 1 ) / 4

n = 28 / 4

n = 7

Youur fraction is:

n / d = 7 / 9

Chesk result.

when both the numerator and denominator are each decreased by 1

( 7 - 1 ) / ( 9 - 1 ) = 6 / 8 = 3 • 2 / 3 • 4 = 3 / 4

when both the numerator and denominator are each increased by 3

( 7 + 3 ) / ( 9 + 3 ) = 10 / 12 = 2 • 5 / 2 • 6 = 5 / 6