Certainly! Here is a step-by-step solution to determine the son's age based on the given problem:
1. Define Variables:
- Let [tex]\( s \)[/tex] represent the son's current age.
- Let [tex]\( f \)[/tex] represent the father's current age.
2. Set Up Equations:
- According to the information given, the father is four times as old as his son:
[tex]\[
f = 4s
\][/tex]
- In IHyear's time, the father will be twice as old as his son. Since the exact meaning of "IHyear" is unclear, let’s assume there may be a typographical error or ambiguity that we should resolve by checking the options given.
3. Rewrite the Second Condition:
- If we assume "IHyear" means one year (the typical interpretation), then in one year's time:
[tex]\[
f + 1 = 2(s + 1)
\][/tex]
4. Substitute the First Equation into the Second Equation:
[tex]\[
4s + 1 = 2(s + 1)
\][/tex]
5. Solve for [tex]\( s \)[/tex]:
[tex]\[
4s + 1 = 2s + 2
\][/tex]
[tex]\[
4s - 2s = 2 - 1
\][/tex]
[tex]\[
2s = 1
\][/tex]
[tex]\[
s = \frac{1}{2}
\][/tex]
6. Interpret the Solution:
- The solution [tex]\( s = \frac{1}{2} \)[/tex] doesn’t make practical sense, as age should be a whole number. Let’s examine the provided options and check each:
### Verification of Options:
- Option A: [tex]\( s = 6 \)[/tex]
[tex]\[
f = 4 \times 6 = 24
\][/tex]
In one year's time:
[tex]\[
f + 1 = 24 + 1 = 25
\][/tex]
[tex]\[
2(s + 1) = 2(6 + 1) = 2 \times 7 = 14
\][/tex]
Since 25 is not equal to 14, this option is incorrect.
- Option B: [tex]\( s = 8 \)[/tex]
[tex]\[
f = 4 \times 8 = 32
\][/tex]
In one year's time:
[tex]\[
f + 1 = 32 + 1 = 33
\][/tex]
[tex]\[
2(s + 1) = 2(8 + 1) = 2 \times 9 = 18
\][/tex]
Since 33 is not equal to 18, this option is incorrect.
- Option C: [tex]\( s = 22 \)[/tex]
[tex]\[
f = 4 \times 22 = 88
\][/tex]
In one year's time:
[tex]\[
f + 1 = 88 + 1 = 89
\][/tex]
[tex]\[
2(s + 1) = 2(22 + 1) = 2 \times 23 = 46
\][/tex]
Since 89 is not equal to 46, this option is incorrect.
- Option D: [tex]\( s = 36 \)[/tex]
[tex]\[
f = 4 \times 36 = 144
\][/tex]
In one year's time:
[tex]\[
f + 1 = 144 + 1 = 145
\][/tex]
[tex]\[
2(s + 1) = 2(36 + 1) = 2 \times 37 = 74
\][/tex]
Since 145 is not equal to 74, this option is incorrect.
Since none of the given options fit the conditions when "IHyear" is assumed to be one year, it suggests that there might be an issue with the interpretation of "IHyear," or there may be a mistake in the options provided. Given the problem constraints, we deduce that none of the options correctly solve the problem. Therefore, the conclusion is:
None of the options provided are correct.
