Ben, Henry and Japheth had a total of 37 beads. The ratio of the number of beads that Henry had to the number of beads that Japheth had was 6 : 5. After Ben and Henry each gave away half of their beads, the 3 children had 26 beads left. How many beads did Henry and Japheth have in the end?
| |
Ben |
Henry |
Japheth |
Total |
| Before |
2 p |
6 u |
5 u |
37 |
| Change |
- 1 p |
- 3 u |
|
- 11 |
| After |
1 p |
3 u |
5 u |
26 |
Total number of beads that Ben and Henry gave away
= 37 - 26
= 11
1 p + 3 u = 11 --- (1)
1 p + 3 u + 5 u = 26
1 p + 8 u = 26 --- (2)
(2) - (1)
(1 p + 8 u) - (1 p + 3 u) = 26 - 11
8 u - 3 u = 15
5 u = 15
1 u = 15 ÷ 5 = 3
Total number of beads that Henry and Japheth had in the end
= 3 u + 5 u
= 8 u
= 8 x 3
= 24
Answer(s): 24
