Question

Work out the value of z, given that x+y=42 and x/13=y/8=z/9.

Answer 1

z = 18

x = 26 and y = 16

Explanation:

Given:

`x + y = 42`

`(x)/(13)=(y)/(8)=(z)/(9)`

Rewrite
`x + y = 42` to make
`y` the subject:

`\implies y=42-x`

Substitute this into
`(x)/(13)=(y)/(8)`:

`\implies (x)/(13)=(42-x)/(8)`

Cross multiply:

`\implies 8x=13(42-x)`

`\implies 8x=546-13x`

`\implies 21x=546`

`\implies x=26`

Substitute found value of x into
`x + y = 42` and solve for y:

`\implies 26 + y = 42`

`\implies y=16`

Substitute found value of y into
`(y)/(8)=(z)/(9)` and solve for z:

`\implies (16)/(8)=(z)/(9)\\\\\implies 2=(z)/(9)\\\\\implies 18=z`