Elijah, David and Ryan had a total of 74 beads. The ratio of the number of beads that David had to the number of beads that Ryan had was 4 : 3. After Elijah and David each gave away half of their beads, the 3 children had 52 beads left. How many beads did David and Ryan have at first?
| |
Elijah |
David |
Ryan |
Total |
| Before |
2 p |
4 u |
3 u |
74 |
| Change |
- 1 p |
- 2 u |
|
- 22 |
| After |
1 p |
2 u |
3 u |
52 |
Total number of beads that Elijah and David gave away
= 74 - 52
= 22
1 p + 2 u = 22 --- (1)
1 p + 2 u + 3 u = 52
1 p + 5 u = 52 --- (2)
(2) - (1)
(1 p + 5 u) - (1 p + 2 u) = 52 - 22
5 u - 2 u = 30
3 u = 30
1 u = 30 ÷ 3 = 10
Total number of beads that David and Ryan had at first
= 4 u + 3 u
= 7 u
= 7 x 10
= 70
Answer(s): 70
