Question

64 coins is distributed between A and B such that ${\frac{1}{5}}^{th}$ of the number of gold coins received by A is equal to ${\frac{1}{3}}^{rd}$ of the number of gold coins received by B. How do we represent this using a linear equation in single variable?

Answer 1

Number of coins received by A = $x$
Hence, the number of coins received by B will be $64-x$ [1 mark]
Now ${\frac{1}{5}}^{th}$ of the number of coins received by A = $\frac{1}{5}timesx=\frac{x}{5}$
and ${\frac{1}{3}}^{rd}$ of the number of coins received by B = $\frac{1}{3}times\frac{64-x}{3}$ [1 mark]
Since the above two quantities are equal, $\frac{x}{5}=\frac{64-x}{3}$ [1 mark]