Question

The difference of two numbers is 16. But large number is five less than four times the smaller number. Find the two numbers.

Answer 1

Let x be the larger number and y be the smaller number.

Given the difference between two numbers is 16.

$x-y=16\ldots\text{..}(1)$

Given larger number is five less than four times the smaller number.

$x=4y-5\ldots\text{.}\mathrm{}(2)$

Now, solve the equation (1)

$x=16+y$

Put x in the 2nd equation.

$\begin{gathered} 16+y=4y-5 \\ 4y-y=16+5 \\ 3y=21 \end{gathered}$

Further solved as,

$y=7$

Now, put the value of y in equation (1)

$\begin{gathered} x-y=16 \\ x-7=16 \\ x=16+7 \\ x=23 \end{gathered}$

Thus,

$x=23$

Therefore, the two numbers are 23 and 7.