Question

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

Answer 1

Answer:

z = 18

x = 26 and y = 16

Step-by-step explanation:

Given:

$x + y = 42$

$\dfrac{x}{13}=\dfrac{y}{8}=\dfrac{z}{9}$

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

$\implies y=42-x$

Substitute this into $\dfrac{x}{13}=\dfrac{y}{8}$:

$\implies \dfrac{x}{13}=\dfrac{42-x}{8}$

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 $\dfrac{y}{8}=\dfrac{z}{9}$ and solve for z:

$\implies \dfrac{16}{8}=\dfrac{z}{9}\\\\\implies 2=\dfrac{z}{9}\\\\\implies 18=z$