Valen, Elijah and Japheth shared a bag of beads. Elijah took 35 as many beads as Japheth. Valen took twice as many beads as the total Elijah and Japheth took. After Valen had given 50 to Elijah and 22 to Japheth, Elijah gave 5 to Japheth. In the end, all three of them had the same number of beads. Find the difference between the number of beads that Valen and Elijah had at first.
| |
Elijah |
Japheth |
Valen |
Total |
| Before |
3 u |
5 u |
16 u |
24 u |
| Change 1 |
+ 50 |
|
- 50 |
|
| Change 2 |
|
+ 22 |
- 22 |
|
| Change 3 |
- 5 |
+ 5 |
|
|
| After |
1x8 =
8 u |
1x8 =
8 u |
1x8 =
8 u |
3x8 =
24 u |
Total number of beads that Elijah and Japheth had at first
= 3 u + 5 u
= 8 u
Number of beads that Valen had at first
= 2 x 8 u
= 16 u
The total number of beads remains unchanged. Make the total number of beads the same. LCM of 3 and 24 is 24.
Number of beads that Japheth received from Elijah and Valen
= 8 u - 5 u
= 3 u
3 u = 22 + 5
3 u = 27
1 u = 27 ÷ 3 = 9
Difference between the number beads that Valen and Elijah had at first
= 16 u - 3 u
= 13 u
= 13 x 9
= 117
Answer(s): 117
