Question

Use a system of equations to solve the following problem.The sum of three integers is 244. The sum of the first and second integers exceeds the third by 48. The third integer is 36 less than the first Findthe three integersAnswer How to enter your answer topens in new windon 5 PointsKeypadKeyboard Shartofirst integer =second integer =third integer =

Answer 1

Given:

The sum of three integers is 244. The sum of the first and second integers exceeds the third by 48. The third integer is 36 less than the first.

Aim:

We need to find the values of all three integers.

Step-by-step explanation:

Let x be the first integer.

Let y be the second integer.

Let z be the third interger.

The sum of three integers is 244.

`x+y+z=244`

The sum of the first and second integers exceeds the third by 48.

`x+y=z+48`

The third integer is 36 less than the first.

`z=x-36`

Substitute z=x-36 in the equation x+y=z-48 .

`x+y=x-36+48`

`x+y=x+12`

Subtract x from both sides of the equation.

`x+y-x=x+12-x`
`y=12`

Substitute z=x-36 and y=12 in the equation x+y+z=244.

`x+12+x-36=244`

Add 24 to both sides of the equation.

`2x-24+24=244+24`

`2x=268`

Divide both sides by 2.

`(2x)/(2)=(268)/(2)`
`x=134`

Substitute x=134 in the equation z=x-36

`z=134-36`
`z=98`

We get x=128, y=12 and z =98.

Final answer:

first integer = 128

second integer =`12

third integer = 98.