In April, Fanny and Brandon had beads in the ratio 10 : 9. In May, each of them gave away the same number of beads. Fanny then had thrice as many beads as Brandon.

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

	Fanny	Brandon	Difference
Before	10x2 = 20 u	9x2 = 18 u	1x2 = 2 u
Change	- 17 u	- 17 u
After	3x1 = 3 u	1x1 = 1 u	2x1 = 2 u

(a)
Since Fanny and Brandon gave away the same number of beads, the difference in the number of beads between Fanny 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 1 and 2 is 2.

Brandon's beads in April : Brandon's beads in May
18 : 1

(b)
Total number of beads in April
= 20 u + 18 u
= 38 u

Total number of beads in May
= 3 u + 1 u
= 4 u

Total beads in April : Total beads in May
38 : 4 _(÷2)
19 : 2 

Answer(s): (a) 18 : 1; (b) 19 : 2