Justin and Elijah shared some beads in the ratio of 5 : 8. After both each gave away 6 beads to their brother, the ratio of the number of beads Justin had to the total number of beads left was 1 : 3. How many beads did the two boys have at first?
|
Justin |
Elijah |
Difference |
Before |
5x1 = 5 u |
8x1 = 8 u |
3x1 = 3 u |
Change |
- 6 |
- 6 |
|
After |
1x3 = 3 u |
2x3 = 6 u |
1x3 = 3 u |
Number of beads that Justin and Elijah each gave to their brother is the same.
The difference in the number of beads at first and in the end between Justin and Elijah remains unchanged. Make the difference in the number of beads the same. LCM of 3 and 1 is 3.
Number of beads that Justin gave to their brother
= 5 u - 3 u
= 2 u
2 u = 6
1 u = 6 ÷ 2 = 3
Number of beads that the two boys had at first
= 5 u + 8 u
= 13 u
= 13 x 3
= 39
Answer(s): 39