To solve this problem, let's define the variables and use the given information in a step-by-step manner:
1. Define variables:
- Let "A" represent Alison's current age.
- Let "F" represent her father's current age.
2. According to the problem:
- Alison is 26 years younger than her father. Therefore, we can state:
[tex]\[
F = A + 26
\][/tex]
3. Future ages in 4 years:
- In 4 years, Alison's age will be [tex]\(A + 4\)[/tex].
- In 4 years, her father's age will be [tex]\(F + 4\)[/tex].
4. Condition given in the problem:
- Her father's age in 4 years will be 3 times Alison's age in 4 years. Mathematically, this can be expressed as:
[tex]\[
F + 4 = 3 \times (A + 4)
\][/tex]
5. Substitute the expression for [tex]\(F\)[/tex] from step 2:
- Substitute [tex]\(F = A + 26\)[/tex] into the equation [tex]\(F + 4 = 3 \times (A + 4)\)[/tex]:
[tex]\[
(A + 26) + 4 = 3 \times (A + 4)
\][/tex]
6. Simplify and solve for [tex]\(A\)[/tex]:
[tex]\[
A + 26 + 4 = 3(A + 4)
\][/tex]
[tex]\[
A + 30 = 3A + 12
\][/tex]
- Bring all terms involving [tex]\(A\)[/tex] to one side:
[tex]\[
A + 30 - 12 = 3A
\][/tex]
[tex]\[
18 = 2A
\][/tex]
- Divide both sides by 2 to solve for [tex]\(A\)[/tex]:
[tex]\[
A = 9
\][/tex]
Therefore, Alison is currently 9 years old.
7. Verification:
- If Alison is 9 years old, her father's current age, [tex]\(F\)[/tex], is:
[tex]\[
F = A + 26 = 9 + 26 = 35
\][/tex]
- In 4 years, Alison's age will be [tex]\(9 + 4 = 13\)[/tex] and her father's age will be [tex]\(35 + 4 = 39\)[/tex].
- Checking the condition: Is 39 three times 13?
[tex]\[
39 = 3 \times 13
\][/tex]
- Yes, it is correct.
Thus, the solution is verified, and Alison is 9 years old.
