Three sisters have ages that are consecutive odd integers. The sum of the age of the youngest and three times the age of the oldest is five less than five times the middle sister’s age.

youngest   17  

middle  19

oldest    21

Step-by-step explanation:

Three sisters have ages that are consecutive odd integers

youngest = x

middle = x + 2

oldest = x + 4

The sum of the age of the youngest

x

and three times the age of the oldest

+ 3(x + 4)

is five less than five times the middle sister’s age

= 5(x + 2) - 5

x + 3(x + 4) = 5(x + 2) - 5

Distribute

x + 3x + 12 = 5x + 10 - 5

Combine like terms

4x + 12 = 5x - 5

Subtract 4x from both sides

12 = x - 5

Add 5 to both sides

17 = x

youngest   x = 17  

middle     x + 2 = 19

oldest     x + 4 = 21