Question

Two sisters have ages that are consecutive odd integers. When the younger one doubles her age and the older one triples her age, the sum of the results is 121. What are their ages?

a) Younger sister is 33, older sister is 35.
b) Younger sister is 37, older sister is 39.
c) Younger sister is 29, older sister is 31.
d) Younger sister is 25, older sister is 27.

Answer 1

After setting up and solving the equation based on the information given, we find that the younger sister's age should be 23 and the older sister's age should be 25 years old. However, these ages are not listed in the provided options, indicating a possible typo in the question.

Step-by-step explanation:

The question asks us to find the ages of two sisters given that their ages are consecutive odd integers and the sum of twice the younger one's age and three times the older one's age is 121. We can denote the younger sister's age as 'y' and the older sister's age as 'y + 2' (since they are consecutive odd integers, the difference between them will be 2).

To find their ages, we set up an equation based on the information given:
2y + 3(y + 2) = 121.

Let's solve this step by step:
1. Distribute the 3: 2y + 3y + 6 = 121
2. Combine like terms: 5y + 6 = 121
3. Subtract 6 from both sides: 5y = 115
4. Divide by 5: y = 23

So the younger sister is 23 years old, and the older sister is y + 2 = 23 + 2 = 25 years old.

However, none of the options given in the question contain the ages 23 and 25, which suggests there might be a typo in the answer choices provided. Based on our calculation, none of the options is correct.