In May, Rachel and Brandon had beads in the ratio 15 : 8. In June, each of them gave away the same number of beads. Rachel then had five times as many beads as Brandon.

1. Find the ratio of the number of beads Brandon had in May to the number of beads he had in June.
2. Find the ratio of the total number of beads both had in May to the total number of beads both had in June.

	Rachel	Brandon	Difference
Before	15x4 = 60 u	8x4 = 32 u	7x4 = 28 u
Change	- 25 u	- 25 u
After	5x7 = 35 u	1x7 = 7 u	4x7 = 28 u

(a)
Since Rachel and Brandon gave away the same number of beads, the difference in the number of beads between Rachel and Brandon at first and in the end remains the same.

Make the difference in the number of beads at first and in the end the same. LCM of 7 and 4 is 28.

Brandon's beads in May : Brandon's beads in June
32 : 7

(b)
Total number of beads in May
= 60 u + 32 u
= 92 u

Total number of beads in June
= 35 u + 7 u
= 42 u

Total beads in May : Total beads in June
92 : 42 _(÷2)
46 : 21 

Answer(s): (a) 32 : 7; (b) 46 : 21