Carl, Daniel and Tom had a total of 74 beads. The ratio of the number of beads that Daniel had to the number of beads that Tom had was 2 : 3. After Carl and Daniel each gave away half of their beads, the 3 children had 52 beads left. How many beads did Daniel and Tom have in the end?
| |
Carl |
Daniel |
Tom |
Total |
| Before |
2 p |
2 u |
3 u |
74 |
| Change |
- 1 p |
- 1 u |
|
- 22 |
| After |
1 p |
1 u |
3 u |
52 |
Total number of beads that Carl and Daniel gave away
= 74 - 52
= 22
1 p + 1 u = 22 --- (1)
1 p + 1 u + 3 u = 52
1 p + 4 u = 52 --- (2)
(2) - (1)
(1 p + 4 u) - (1 p + 1 u) = 52 - 22
4 u - 1 u = 30
3 u = 30
1 u = 30 ÷ 3 = 10
Total number of beads that Daniel and Tom had in the end
= 1 u + 3 u
= 4 u
= 4 x 10
= 40
Answer(s): 40
