Tommy, Ryan and Caden had a total of 45 beads. The ratio of the number of beads that Ryan had to the number of beads that Caden had was 2 : 3. After Tommy and Ryan each gave away half of their beads, the 3 children had 33 beads left. How many beads did Ryan and Caden have in the end?
| |
Tommy |
Ryan |
Caden |
Total |
| Before |
2 p |
2 u |
3 u |
45 |
| Change |
- 1 p |
- 1 u |
|
- 12 |
| After |
1 p |
1 u |
3 u |
33 |
Total number of beads that Tommy and Ryan gave away
= 45 - 33
= 12
1 p + 1 u = 12 --- (1)
1 p + 1 u + 3 u = 33
1 p + 4 u = 33 --- (2)
(2) - (1)
(1 p + 4 u) - (1 p + 1 u) = 33 - 12
4 u - 1 u = 21
3 u = 21
1 u = 21 ÷ 3 = 7
Total number of beads that Ryan and Caden had in the end
= 1 u + 3 u
= 4 u
= 4 x 7
= 28
Answer(s): 28
