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.