Question

The sum of two numbers is 40. If the larger is divided by the smaller, the quotient is 5 and the remainder is 4. Find the number.

Answer 1

`x=36`

`y=6`

Explanation:

Let x be the large number and y be the small number.

Given:

The sum of two numbers is 40.

So the first relation is.

`x+y=40`---------(1)

The large value is divided by smaller value.

So,
`(x)/(y)`, and the quotient is 5 and the remainder is 4.

and second relation is.

`(x)/(y) =5+(4)/(y)`

`(x)/(y) =(5y+4)/(y)`

The denominator y is cancelled both side.

`x = 5y + 4`

x value put in the equation 1

`5y+4+y=40`

`6y=40-4\\y=(36)/(6) \\y=6`

Put y value in equation 1

`x+6=40`

`x=40-6`

`x=36`

Therefore, x value is 36 and y value is 6.