In March, Cathy and Jeremy had beads in the ratio 2 : 1. In April, each of them gave away the same number of beads. Cathy then had five times as many beads as Jeremy.

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

	Cathy	Jeremy	Difference
Before	2x4 = 8 u	1x4 = 4 u	1x4 = 4 u
Change	- 3 u	- 3 u
After	5x1 = 5 u	1x1 = 1 u	4x1 = 4 u

(a)
Since Cathy and Jeremy gave away the same number of beads, the difference in the number of beads between Cathy and Jeremy 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 4 is 4.

Jeremy's beads in March : Jeremy's beads in April
4 : 1

(b)
Total number of beads in March
= 8 u + 4 u
= 12 u

Total number of beads in April
= 5 u + 1 u
= 6 u

Total beads in March : Total beads in April
12 : 6 _(÷6)
2 : 1 

Answer(s): (a) 4 : 1; (b) 2 : 1