Question

The sum of three integers is 280. The sum of the first and second integers exceeds the third by 34. The third integer is 30 less than the first. Find the three integers.

Answer 1

Answer:

The sum of three integers is 280.

a + b + c = 280

;

The sum of the first and second integers exceeds the third by 70.

a + b = c + 70

:

the third integer is 21 less than the first.

c = a - 21

:

Rearrange the 2nd equation and use elimination with the 1st equation

a + b + c = 280

a + b - c = 70

------------------subtraction eliminates a & b, find c

0 + 0 + 2c = 210

c = 210/2

c = 105

then

105 = a - 21

a = 105 + 21

a = 126

Find b using the 1st equation

126 + b + 105 = 280

b = 280 - 231

b = 49

:

:

See if that checks out

126 + 49 + 105 = 280

:

the three integers. 126, 49, 105