At the beginning of the year, the number of members in Club S and Club T were in the ratio 4 : 5. At the end of Term One, some members left Club S to join Club T. The ratio of the number of members in Club S and Club T became 2 : 3. In the middle of Term Two, each club received 45 new members. The ratio of the number of members in Club S and Club T became 3 : 4. How many members left Club S to join Club T at the end of Term One?
| |
Club S |
Club T |
Total |
Difference |
Start of Term One |
4x5 =
20 u |
5x5 =
25 u |
9x5 =
45 u |
|
| Change 1 |
- ? |
+ ? |
|
|
End of Term One |
2x9 =
18 u |
3x9 =
27 u |
5x9 =
45 u |
1x9 =
9 u |
| Change 2 |
+ 45 |
+ 45 |
|
|
End of Term Two |
3x9 =
27 u |
4x9 =
36 u |
|
1x9 =
9 u |
The total at first and in the end of Term One remains unchanged. Make the total at first and in the end of Term One the same. LCM of 5 and 9 is 45.
The difference at the end of Term One and Term Two remains unchanged. Make the difference at the end of Term One and Term Two the same. LCM of 9 and 1 is 9.
Number of members that each club received in the middle of Term Two
= 27 u - 18 u
= 9 u
9 u = 45
1 u = 45 ÷ 9 = 5
Number of members who left Club S to join Club T at the end of Term One
= 20 u - 18 u
= 2 u
= 2 x 5
= 10
Answer(s): 10
