Question

Use a system of equations to solve the following problem.The sum of three integers is 380. The sum of the first and second integers exceeds the third by 74. Thethird integer is 62 less than the first. Find the three integers.AnswerHow to enter your answer (Opens in new window)KeypadKeyboard Shortcutfirst integer =second integer =third integer =

Answer 1

Let x represent the first integer.

Let y represent the second integer.

Let z represent the third integer.

From the information given,

the sum of the three integers is 380. This means that

x + y + z = 380

The sum of the first and second integers exceeds the third by 74. This means that

x + y = z + 74

The third integer is 62 less than the first. This means that

z = x - 62

We would substitute z = x - 62 into the first and second equations. We have

For the first equation,

x + y + x - 62 = 380

By collecting like terms, we have

x + x + y = 380 + 62

2x + y = 442

For the second equation,

x + y = x - 62 + 74

By collecting like terms,

x - x + y = - 62 + 74

y = 12

Subctituting y = 12 into 2x + y = 442, we have

2x + 12 = 442

2x = 442 - 12 = 430

x = 430/2

x = 215

z = x - 62 = 215 - 62

z = 153

Thus, the integers are 215, 12 and 153