Question

There are three integers. The quotient of the first number and the third number is 13. If the first number was three more, then it would be double the sum of the second and third number, combined. The sum of all the numbers is 21. What are the numbers?

Answer 1

Given:

There are three integers.

The quotient of the first number and the third number is 13.

If the first number was three more, then it would be double the sum of the second and third number, combined.

The sum of all the numbers is 21.

To find:

The all three numbers.

Solution:

Let the three numbers are x, y and z.

The quotient of the first number and the third number is 13.

`(x)/(z)=13`

`x=13z` ...(i)

If the first number was three more, then it would be double the sum of the second and third number, combined.

`(x+3)=2(y+z)`

`13z+3=2y+2z` [Using (i)]

`13z+3-2z=2y`

`11z+3=2y`

Divide both sides by 2.

`(11z+3)/(2)=y` ...(ii)

The sum of all the numbers is 21.

`x+y+z=21`

`13z+(11z+3)/(2)+z=21` [Using (i) and (ii)]

Multiply both sides by 2.

`26z+11z+3+2z=42`

`39z=42-3`

`39z=39`

`z=1`

Now,

`x=13(1)=13` [Using (i)]

`y=(11(1)+3)/(2)` [Using (ii)]

`y=(14)/(2)`

`y=7`

Therefore, x=13, y=7 and z=1.