Rael, Julian and Riordan shared a bag of coins. Julian took 35 as many coins as Riordan. Rael took twice as many coins as the total Julian and Riordan took. After Rael had given 22 to Julian and 10 to Riordan, Julian gave 2 to Riordan. In the end, all three of them had the same number of coins. Find the difference between the number of coins that Rael and Julian had at first.
| |
Julian |
Riordan |
Rael |
Total |
| Before |
3 u |
5 u |
16 u |
24 u |
| Change 1 |
+ 22 |
|
- 22 |
|
| Change 2 |
|
+ 10 |
- 10 |
|
| Change 3 |
- 2 |
+ 2 |
|
|
| After |
1x8 =
8 u |
1x8 =
8 u |
1x8 =
8 u |
3x8 =
24 u |
Total number of coins that Julian and Riordan had at first
= 3 u + 5 u
= 8 u
Number of coins that Rael had at first
= 2 x 8 u
= 16 u
The total number of coins remains unchanged. Make the total number of coins the same. LCM of 3 and 24 is 24.
Number of coins that Riordan received from Julian and Rael
= 8 u - 5 u
= 3 u
3 u = 10 + 2
3 u = 12
1 u = 12 ÷ 3 = 4
Difference between the number coins that Rael and Julian had at first
= 16 u - 3 u
= 13 u
= 13 x 4
= 52
Answer(s): 52
