Alice, Bob and Carol
Three friends, Alice, Bob, and Carol, are comparing their ages. Alice is twice as old as Bob, and Carol is three years older than Bob. The sum of their ages is 45 years. How old is each person?
Take your time to set up equations based on the given information and solve for the ages of Alice, Bob, and Carol.
Let's denote the ages of Alice, Bob, and Carol as A, B, and C respectively.
ReplyDeleteWe have three pieces of information:
Alice is twice as old as Bob: A = 2B
Carol is three years older than Bob: C = B + 3
The sum of their ages is 45 years: A + B + C = 45
Now we can substitute the expressions from the first two points into the third equation:
A + B + C = 45
(2B) + B + (B + 3) = 45
4B + 3 = 45
4B = 42
B = 10.5
Now that we know Bob's age, we can find Alice's age using the first equation:
A = 2B = 2 * 10.5 = 21
And we can find Carol's age using the second equation:
C = B + 3 = 10.5 + 3 = 13.5
So, the ages of Alice, Bob, and Carol are 21 years, 10.5 years, and 13.5 years respectively.