Question

If from twice the greater of two numbers $16$ is subtracted, the result is half the other number. If from half the greater number $1$ is subtracted, the result is still half the other number. What are the numbers?

Answer 1

Let’s consider the greater number to be $x$ and the smaller number to be $y$.

Then, according to the given conditions we have

$2x–16=\frac{y}{2}\Rightarrow 4x-32=y\Rightarrow 4x-y=32$ … (i)

And,

$\frac{x}{2}-1=\frac{y}{2}\Rightarrow x-2=y\Rightarrow x-y=2$ … (ii)

Now, subtracting (ii) from (i) we get

$(4x-y)-(x-y)=32-2$

$\Rightarrow 3x=30$

$\Rightarrow x=10$

On substituting the value of $x$ in (i), we get

$2\left(10\right)-16=\frac{y}{2}$

$\Rightarrow 20-16=\frac{y}{2}$

$\Rightarrow 4=\frac{y}{2}$

$\Rightarrow y=8$

Therefore, the two numbers are $10$ and $8$.