Question

If `x/y = 3(1)/3`, find the value of `(x - 3y)/(2x - 5y)`.

Answer 1

`x/y = 3(1)/3`

Convert the mixed fraction:

`3(1)/3 = 3 + 1/3`

= `(3 xx 3 + 1)/3`

= `10/3`

`x/y = 10/3`

The expression we need to evaluate is `(x - 3y)/(2x - 5y)`

To express this in terms of `x/y`, divide both the numerator and the denominator by y.

`(x - 3y)/(2x - 5y)`

= `((x -3y)/y)/((2x - 5y)/y)`

= `(x/y - (3y)/y)/((2x)/y - (5y)/y)`

= `(x/y - 3)/(2x/y - 5)`

Substitute `x/y = 10/3` into the simplified expression:

`(10/3 - 3)/(2(10/3) - 5)`

= `(10/3 - 9/3)/(20/3 - 15/3)`

= `(1/3)/(5/3)`

`1/3 xx 3/5`

= `1/5`

The value of `(x - 3y)/(2x - 5y)` is `1/5`