Billy, Simon and Jeremy shared a bag of cards. Simon took 25 as many cards as Jeremy. Billy took twice as many cards as the total Simon and Jeremy took. After Billy had given 45 to Simon and 11 to Jeremy, Simon gave 5 to Jeremy. In the end, all three of them had the same number of cards. Find the difference between the number of cards that Billy and Simon had at first.
| |
Simon |
Jeremy |
Billy |
Total |
| Before |
2 u |
5 u |
14 u |
21 u |
| Change 1 |
+ 45 |
|
- 45 |
|
| Change 2 |
|
+ 11 |
- 11 |
|
| Change 3 |
- 5 |
+ 5 |
|
|
| After |
1x7 =
7 u |
1x7 =
7 u |
1x7 =
7 u |
3x7 =
21 u |
Total number of cards that Simon and Jeremy had at first
= 2 u + 5 u
= 7 u
Number of cards that Billy had at first
= 2 x 7 u
= 14 u
The total number of cards remains unchanged. Make the total number of cards the same. LCM of 3 and 21 is 21.
Number of cards that Jeremy received from Simon and Billy
= 7 u - 5 u
= 2 u
2 u = 11 + 5
2 u = 16
1 u = 16 ÷ 2 = 8
Difference between the number cards that Billy and Simon had at first
= 14 u - 2 u
= 12 u
= 12 x 8
= 96
Answer(s): 96
