Question

The sum of three integers is 189. The first integer is 28 less than the second. The second integer is 21 less than the sum of the first and third integer. Find the three integers

Answer 1

The first integer is 56

The second integer is 84

The third integer is 49

Explanation:

Define the variables

Let

x ----> the first integer

y ----> the second integer

z ----> the third integer

we know that

`x+y+z=189` ----> equation A

`x=y-28` ---->
`y=x+28` ----> equation B

`y=(x+z)-21` ----> equation C

Equate equations B and C

`(x+z)-21=x+28`

subtract x both sides

`z-21=28`

Adds 21 both sides

`z=28+21`

`z=49`

substitute the value of z in equation A

`x+y+49=189`

`x+y=189-49`

`x+y=140` -----> equation D

Solve the system of equations B and D

`y=x+28` ----> equation B

`x+y=140` -----> equation D

substitute equation B in equation D and solve for x

`x+x+28=140`

`2x+28=140`

`2x=140-28`

`2x=112`

`x=56`

Find the value of y

`y=x+28` ----->
`y=56+28=84`

therefore

The first integer is 56

The second integer is 84

The third integer is 49