Ratio with Algebra

Algebra Level 2

If

( 2 x + 3 y ) : ( 3 x + 5 y ) = 12 : 19 (2x+3y) :( 3x+5y) = 12 : 19

Find a + b a+b if x y = a b \frac xy = \frac ab , where a a and b b are coprime positive integers.

1.5 5 7 6 2 45 3

Sravanth C. by Sravanth C. , 21, India

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1 solution

Vaibhav Chandan
May 24, 2015

2x + 3y : 3x + 5y = 12 : 19.

By cross multiplying we get:

38x + 57y = 36x + 60y

2x = 3y

x/y = 3/2

a=3, b=2

a+b=5

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