Year 11 Maths - Methods Variation

Joint Variation

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Questions

Question 1

30081

If $y$ varies jointly as $x$ and $z$, and $y = 33$ when $x = 9$ and $z = 12$, find $y$ when $x = 16$ and $z = 36.$

Answer

$y = 176$

Worked Solution

$$
\begin{aligned}
y &\propto x z \\
y&=k \times xz \\
33&=k \times 9 \times 12 \\
k&=\frac{33}{9 \times 12} \\
k&=\frac{11}{36}\\
y &=\frac{11}{36} \times xz \\
&=\frac{11}{36} \times 16 \times 36 \\
y &=176
\end{aligned}
$$

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