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. (a) If x represents the age of the youngest child, then write an equation that models this scenario. (b) Determine the ages of the three sisters.

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

(b) youngest: 7 years old

middle: 9 years old

oldest: 11 years old

Step-by-step explanation:

(a)

We know that x is the youngest child's age. Since the sisters' ages are consecutive odd integers, we know that the ages differ by 2. So, the middle sister's age is x + 2 and the oldest sister's age is x + 4.

Our equation to model the sentence "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" would be:

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

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

(b)

Now, we can just solve the equation above:

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

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

4x + 12 = 5x + 5

x = 12 - 5 = 7

So, the youngest sister is 7 years old.

That means the middle sister is 7 + 2 = 9 years old, and the oldest sister is 9 + 2 = 11 years old.

The ages, then, are:

youngest: 7 years old

middle: 9 years old

oldest: 11 years old