Let's use algebra to solve the problem step by step.
Let \( A \) represent Asher's age. We are given three conditions:
1. Cara is one year older than twice Asher's age, so Cara's age \( C \) can be written as:
\[ C = 2A + 1 \]
2. Brice is 22 years older than Asher, so Brice's age \( B \) can be written as:
\[ B = A + 22 \]
3. The total of their three ages is 167, so we can write:
\[ A + C + B = 167 \]
Now we can substitute \( C \) and \( B \) with the expressions we have in terms of \( A \):
\[ A + (2A + 1) + (A + 22) = 167 \]
Combine like terms:
\[ 4A + 23 = 167 \]
Now, isolate the variable \( A \) by subtracting 23 from both sides:
\[ 4A = 167 - 23 \]
\[ 4A = 144 \]
Divide by 4 to solve for \( A \):
\[ A = \frac{144}{4} \]
\[ A = 36 \]
Now that we have Asher's age, let's find Cara's age:
\[ C = 2A + 1 \]
\[ C = 2(36) + 1 \]
\[ C = 72 + 1 \]
\[ C = 73 \]
Finally, let's find Brice's age:
\[ B = A + 22 \]
\[ B = 36 + 22 \]
\[ B = 58 \]
In conclusion:
- Asher is 36 years old.
- Cara is 73 years old.
- Brice is 58 years old.
These are the ages of Asher, Cara, and Brice respectively.
