Rael, Ian and Cody shared a bag of cards. Ian took 35 as many cards as Cody. Rael took twice as many cards as the total Ian and Cody took. After Rael had given 29 to Ian and 11 to Cody, Ian gave 4 to Cody. In the end, all three of them had the same number of cards. Find the difference between the number of cards that Rael and Ian had at first.
| |
Ian |
Cody |
Rael |
Total |
| Before |
3 u |
5 u |
16 u |
24 u |
| Change 1 |
+ 29 |
|
- 29 |
|
| Change 2 |
|
+ 11 |
- 11 |
|
| Change 3 |
- 4 |
+ 4 |
|
|
| After |
1x8 =
8 u |
1x8 =
8 u |
1x8 =
8 u |
3x8 =
24 u |
Total number of cards that Ian and Cody had at first
= 3 u + 5 u
= 8 u
Number of cards that Rael had at first
= 2 x 8 u
= 16 u
The total number of cards remains unchanged. Make the total number of cards the same. LCM of 3 and 24 is 24.
Number of cards that Cody received from Ian and Rael
= 8 u - 5 u
= 3 u
3 u = 11 + 4
3 u = 15
1 u = 15 ÷ 3 = 5
Difference between the number cards that Rael and Ian had at first
= 16 u - 3 u
= 13 u
= 13 x 5
= 65
Answer(s): 65
