To solve the problem, let's use the information given step by step to determine Andy and Lori's ages.
1. Define the variables:
- Let [tex]\( L \)[/tex] represent Lori's age.
2. Since Andy is seven years older than Lori, Andy's age can be expressed in terms of Lori's age:
- Andy's age [tex]\( A \)[/tex] = [tex]\( L + 7 \)[/tex].
3. According to the problem, the sum of Lori and Andy's ages is fifty-one:
- [tex]\( L + A = 51 \)[/tex].
4. Substitute Andy's age in the equation from step 3:
- [tex]\( L + (L + 7) = 51 \)[/tex].
5. Combine like terms to simplify the equation:
- [tex]\( 2L + 7 = 51 \)[/tex].
6. Solve for [tex]\( L \)[/tex] by isolating the variable:
- First, subtract 7 from both sides:
[tex]\[
2L = 51 - 7 \\
2L = 44
\][/tex]
- Next, divide both sides by 2:
[tex]\[
L = \frac{44}{2} \\
L = 22
\][/tex]
7. Now that we know Lori's age [tex]\( L \)[/tex] is 22, calculate Andy's age by adding 7 to Lori's age:
[tex]\[
A = L + 7 \\
A = 22 + 7 \\
A = 29
\][/tex]
Therefore, Lori is 22 years old and Andy is 29 years old.
