Valen and Sean had some beads in the ratio of 7 : 6. Sean and Tommy had some beads in the ratio of 4 : 1. Valen sold 32 beads to Tommy and ended up with half the number of beads Sean had. How many beads did Tommy have in the end?
| Valen |
Sean |
Tommy |
| 7x2 |
6x2 |
|
| |
4x3 |
1x3 |
| 14 u |
12 u |
3 u |
The number of beads that Sean had at first is repeated. Make the number of beads that Sean had at first the same. LCM of 6 and 4 is 12.
| |
Valen |
Sean |
Tommy |
| Before |
14 u |
12 u |
3 u |
| Change |
- 32 |
|
+ 32 |
| After |
6 u |
12 u |
3 u + 32 |
Number of beads that Valen had in the end
= 12 u ÷ 2
= 6 u
Number of beads that Valen sold to Tommy
= 14 u - 6 u
= 8 u
8 u = 32
1 u = 32 ÷ 8 = 4
Number of beads that Tommy had in the end
= 3 u + 32
= 3 x 4 + 32
= 12 + 32
= 44
Answer(s): 44
