Question

Use a system of equations to solve the following problem.The sum of three integers is380. The sum of the first and second integers exceeds the third by74. The third integer is62 less than the first. Find the three integers.

Answer 1

the three integers are 215, 12 and 153

Step-by-step explanation:

Let the three integers = x, y, and z

x + y + z = 380 ....equation 1

The sum of the first and second integers exceeds the third by 74:

x + y - 74 = z

x + y - z = 74 ....equation 2

The third integer is 62 less than the first:

x - 62 = z ...equation 3

subtract equation 2 from 1:

x -x + y - y + z - (-z) = 380 - 74

0 + 0 + z+ z = 306

2z = 306

z = 306/2

z = 153

Insert the value of z in equation 3:

x - 62 = 153

x = 153 + 62

x = 215

Insert the value of x and z in equation 1:

215 + y + 153 = 380

368 + y = 380

y = 380 - 368

y = 12

Hence, the three integers are 215, 12 and 153