Question

What number should be added to the terms of 49:68 to get the ratio of 3:4 ? I need the answer with steps.

Answer 1

$Let\ the\ number\ to\ be\ added\ be\ x.\ Thus\\ \\ \frac{49+x}{68+x} = \frac{3}{4} \\ \\ 4(49+x)=3(68+x)\\ \\196+4x=204+3x\\ \\4x-3x=204-196\\ \\x=\boxed8\\ \\So\ 8\ should\ be\ added\ to\ the\ terms\ of\ 49:68\ to\ get\ the\ ratio\ 3:4.$

Answer 2

let the number be y
49+y/68+y=3/4
After cross multiplication
4(49+y)=3(68+y)
196+4y=204+3y
204-196=4y-3y
8=y