"The sum of three numbers is 69."

a + b + c = 69

"the second number is equal to the first diminished by 8"

b = a - 8

he 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 is the number?

"the third number is 5 times the first"

c = 5a

a + (a-8) + (5a) = 69

7a = 77

a = 11

b = 11 - 8 = 3

c = 5·11 = 55

Check: 

a + b + c = 11 + 3 + 55 = 69 answer