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scZoUnD [109]
2 years ago
12

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

Mathematics
1 answer:
Andru [333]2 years ago
4 0

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

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