Question

Use a system of equations to solve the following problem.

The sum of three integers is 45. The sum of the first and second integers exceeds the third by 69. The third integer is 65 less than the first. Find the three integers.

Answer 1

53, 4, -12

Explanation:

Let the first, second, and third integers be a, b, and c, respectively.

a + b + c = 45

a + b = c + 69

c = a - 65

Using the third equation, substitute the value of c, a - 65, for c in the first two equations.

a + b + a - 65 = 45

a + b = a - 65 + 69

2a + b = 110

b = 4

2a + 4 = 110

2a = 106

a = 53

c = a - 65

c = 53 - 65

c = -12

a = 53; b = 4; c = -12

Answer: 53, 4, -12