Xavier, Tommy and Zane shared a bag of stamps. Tommy took 27 as many stamps as Zane. Xavier took four times as many stamps as the total Tommy and Zane took. After Xavier had given 84 to Tommy and 42 to Zane, Tommy gave 6 to Zane. In the end, all three of them had the same number of stamps. Find the difference between the number of stamps that Xavier and Tommy had at first.
| |
Tommy |
Zane |
Xavier |
Total |
| Before |
2 u |
7 u |
36 u |
45 u |
| Change 1 |
+ 84 |
|
- 84 |
|
| Change 2 |
|
+ 42 |
- 42 |
|
| Change 3 |
- 6 |
+ 6 |
|
|
| After |
1x15 =
15 u |
1x15 =
15 u |
1x15 =
15 u |
3x15 =
45 u |
Total number of stamps that Tommy and Zane had at first
= 2 u + 7 u
= 15 u
Number of stamps that Xavier had at first
= 4 x 15 u
= 36 u
The total number of stamps remains unchanged. Make the total number of stamps the same. LCM of 3 and 45 is 45.
Number of stamps that Zane received from Tommy and Xavier
= 15 u - 7 u
= 8 u
8 u = 42 + 6
8 u = 48
1 u = 48 ÷ 8 = 6
Difference between the number stamps that Xavier and Tommy had at first
= 36 u - 2 u
= 34 u
= 34 x 6
= 204
Answer(s): 204
