Question

The sum of three numbers is 69. If the second number is equal to the first diminished by 8, and the third number is 5 times the first. What are the numbers?
If x represents the first number, then which of the following equations could be used to solve the problem?
x = 6x - 8
69 = 6x - 8
69 = 7x - 8?

Answer 1

x + x-8 +5x = 69

simplifies to 7x-8=69

1st number = 11

2nd number = 3

3rd number = 55

Answer 2

Let x,y and z be the three numbers.
The sum of the numbers is 69. Therefore
x + y + z = 69                       (1)

The second number is equal to the first diminished by 8. Therefore
y = x - 8                               (2)

The third number is 5 times the first. herefore
z = 5x                                  (3)

Substitute (2) and (3) into (1).
x + (x - 8) + 5x = 69
x + x - 8 + 5x = 69
7x - 8 = 69
7x = 69 + 8 = 77
x = 77/7 = 11

From (2), y = x-8 = 11-8 = 3
From (3), z = 5x = 5*11 = 55

Answer: The numbers are 11, 3, and 55
 
We showed that 7x - 8 = 69, or that 69 = 7x - 8