At the beginning of the year, the number of members in Club X and Club Y were in the ratio 5 : 8. At the end of Term One, some members left Club X to join Club Y. The ratio of the number of members in Club X and Club Y became 1 : 4. In the middle of Term Two, each club received 1248 new members. The ratio of the number of members in Club X and Club Y became 3 : 4. How many members left Club X to join Club Y at the end of Term One?
| |
Club X |
Club Y |
Total |
Difference |
Start of Term One |
5x5 =
25 u |
8x5 =
40 u |
13x5 =
65 u |
|
| Change 1 |
- ? |
+ ? |
|
|
End of Term One |
1x13 =
13 u |
4x13 =
52 u |
5x13 =
65 u |
3x13 =
39 u |
| Change 2 |
+ 1248 |
+ 1248 |
|
|
End of Term Two |
3x39 =
117 u |
4x39 =
156 u |
|
1x39 =
39 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 13 is 65.
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 39 and 1 is 39.
Number of members that each club received in the middle of Term Two
= 117 u - 13 u
= 104 u
104 u = 1248
1 u = 1248 ÷ 104 = 12
Number of members who left Club X to join Club Y at the end of Term One
= 25 u - 13 u
= 12 u
= 12 x 12
= 144
Answer(s): 144
