Valen, Neave and Vincent shared a bag of marbles. Neave took 27 as many marbles as Vincent. Valen took thrice as many marbles as the total Neave and Vincent took. After Valen had given 45 to Neave and 15 to Vincent, Neave gave 5 to Vincent. In the end, all three of them had the same number of marbles. Find the difference between the number of marbles that Valen and Neave had at first.
| |
Neave |
Vincent |
Valen |
Total |
| Before |
2 u |
7 u |
27 u |
36 u |
| Change 1 |
+ 45 |
|
- 45 |
|
| Change 2 |
|
+ 15 |
- 15 |
|
| Change 3 |
- 5 |
+ 5 |
|
|
| After |
1x12 =
12 u |
1x12 =
12 u |
1x12 =
12 u |
3x12 =
36 u |
Total number of marbles that Neave and Vincent had at first
= 2 u + 7 u
= 12 u
Number of marbles that Valen had at first
= 3 x 12 u
= 27 u
The total number of marbles remains unchanged. Make the total number of marbles the same. LCM of 3 and 36 is 36.
Number of marbles that Vincent received from Neave and Valen
= 12 u - 7 u
= 5 u
5 u = 15 + 5
5 u = 20
1 u = 20 ÷ 5 = 4
Difference between the number marbles that Valen and Neave had at first
= 27 u - 2 u
= 25 u
= 25 x 4
= 100
Answer(s): 100
