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

Question

asked Jun 28, 2023 142k views

1 Answer

Chicago · Answer 1 · 2023-07-02T06:34:16+0000

Answer:

z = 18

x = 26 and y = 16

Explanation:

Given:

x + y = 42

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

Rewrite
x + y = 42 to make
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:

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