Let's solve this problem step-by-step:
1. Define Variables:
- Let [tex]\( S \)[/tex] be the number of stamps Simon originally had.
- Let [tex]\( W \)[/tex] be the number of stamps William originally had.
2. Establish Relationships:
- According to the problem, originally William had 5 times as many stamps as Simon:
[tex]\[
W = 5S
\][/tex]
3. Effect of Giving Stamps:
- When William gives 24 stamps to Simon:
- William's new number of stamps = [tex]\( W - 24 \)[/tex]
- Simon's new number of stamps = [tex]\( S + 24 \)[/tex]
4. Given Condition:
- After giving 24 stamps, the number of William's stamps is twice the number of Simon's stamps:
[tex]\[
W - 24 = 2(S + 24)
\][/tex]
5. Substitute [tex]\( W = 5S \)[/tex] into the Condition:
[tex]\[
5S - 24 = 2(S + 24)
\][/tex]
6. Solve the Equation:
- Begin by expanding and simplifying:
[tex]\[
5S - 24 = 2S + 48
\][/tex]
- Isolate the variable [tex]\( S \)[/tex] on one side of the equation:
[tex]\[
5S - 2S = 48 + 24
\][/tex]
[tex]\[
3S = 72
\][/tex]
- Solve for [tex]\( S \)[/tex]:
[tex]\[
S = 24
\][/tex]
7. Find William’s Original Number of Stamps:
[tex]\[
W = 5S = 5 \times 24 = 120
\][/tex]
Therefore, the number of stamps that William had in the beginning was [tex]\( \boxed{120} \)[/tex].
