linear equations and consecutive integers

Question

Find three consecutive integers such that three times the larger increased by two is equal to five times the smallest increased by three times the middle integer

Answer 1

Call the numbers x, (x + 1), and (x + 2).

 

We have the following equation:

 

3(x + 2) + 2 = 5x + 3(x + 1)

 

3x + 6 + 2 = 5x + 3x + 3

 

3x + 8 = 8x + 3

 

-5x + 8 = 3

 

-5x = -5

 

x = 1

 

The numbers are 1, 2, and 3