Justin, Rael and Andy shared a bag of cards. Rael took 35 as many cards as Andy. Justin took twice as many cards as the total Rael and Andy took. After Justin had given 17 to Rael and 7 to Andy, Rael gave 2 to Andy. In the end, all three of them had the same number of cards. Find the difference between the number of cards that Justin and Rael had at first.
| |
Rael |
Andy |
Justin |
Total |
| Before |
3 u |
5 u |
16 u |
24 u |
| Change 1 |
+ 17 |
|
- 17 |
|
| Change 2 |
|
+ 7 |
- 7 |
|
| Change 3 |
- 2 |
+ 2 |
|
|
| After |
1x8 =
8 u |
1x8 =
8 u |
1x8 =
8 u |
3x8 =
24 u |
Total number of cards that Rael and Andy had at first
= 3 u + 5 u
= 8 u
Number of cards that Justin 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 Andy received from Rael and Justin
= 8 u - 5 u
= 3 u
3 u = 7 + 2
3 u = 9
1 u = 9 ÷ 3 = 3
Difference between the number cards that Justin and Rael had at first
= 16 u - 3 u
= 13 u
= 13 x 3
= 39
Answer(s): 39
