Question

If `a/b = 2/3` and `x/y = 3/4`, find the value of `(4ay - 3bx)/(5ax - 2by)`.

Answer 1

From the given ratios

`a/b = 2/3`

a = `2/3b`

Also,

`x/y = 3/4`

x = `3/4y`

Simplify the numerator:

Substitute the expressions for a and x into the numerator 4ay − 3bx

`4(2/3b)y − 3b(3/4y)`

= `8/3by - 9/4by`

= `(8/3 - 9/4)by`

= `((32 - 27)/12)by`

= `5/12by`

Simplify the denominator:

Substitute the expressions for a and x into the numerator 5ax - 2by

`5(2/3b)(3/4y) - 2by`

= `5(6/12)by - 2by`

= `5(1/2)by - 2by`

= `(5/2 - 2)by`

= `((5 - 4)/2)by`

= `1/2by`

Divide the simplified numerator by the simplified denominator:

`(5/12by)/(1/2by)`

= `5/12 xx 2/1`

= `10/12`

= `5/6`

The value of `(4ay - 3bx)/(5ax - 2by)` is `5/6`.