Caden, Brandon and Pierre had a total of 35 beads. The ratio of the number of beads that Brandon had to the number of beads that Pierre had was 4 : 3. After Caden and Brandon each gave away half of their beads, the 3 children had 22 beads left. How many beads did Brandon and Pierre have at first?
| |
Caden |
Brandon |
Pierre |
Total |
| Before |
2 p |
4 u |
3 u |
35 |
| Change |
- 1 p |
- 2 u |
|
- 13 |
| After |
1 p |
2 u |
3 u |
22 |
Total number of beads that Caden and Brandon gave away
= 35 - 22
= 13
1 p + 2 u = 13 --- (1)
1 p + 2 u + 3 u = 22
1 p + 5 u = 22 --- (2)
(2) - (1)
(1 p + 5 u) - (1 p + 2 u) = 22 - 13
5 u - 2 u = 9
3 u = 9
1 u = 9 ÷ 3 = 3
Total number of beads that Brandon and Pierre had at first
= 4 u + 3 u
= 7 u
= 7 x 3
= 21
Answer(s): 21
