Answer:
the ages of the three sisters are 7, 9, and 11 years old.
Explanation:
Step 1: Assign variables for the ages of the three sisters. Let's say the youngest sister is x years old, the middle sister is x + 2 years old (since they are consecutive odd integers), and the oldest sister is x + 4 years old.
Step 2: Write an equation based on the given information. The sum of the youngest sister's age and three times the age of the oldest sister is five less than five times the middle sister's age. So, we have:
- x + 3(x + 4) = 5(x + 2) - 5
Step 3: Simplify and solve the equation:
- Distribute on the left side: x + 3x + 12 = 5x + 10 - 5
- Combine like terms: 4x + 12 = 5x + 5
- Move the variables to one side and the constants to the other side: 4x - 5x = 5 - 12
- Simplify: -x = -7
- Divide both sides by -1 to solve for x: x = 7
Step 4: Substitute the value of x back into the expressions for the sisters' ages:
- Youngest sister's age: x = 7 years old
- Middle sister's age: x + 2 = 7 + 2 = 9 years old
- Oldest sister's age: x + 4 = 7 + 4 = 11 years old
Therefore, the ages of the three sisters are 7, 9, and 11 years old.