In February, Zara and Michael had beads in the ratio 12 : 7. In March, each of them gave away the same number of beads. Zara then had five times as many beads as Michael.

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

	Zara	Michael	Difference
Before	12x4 = 48 u	7x4 = 28 u	5x4 = 20 u
Change	- 23 u	- 23 u
After	5x5 = 25 u	1x5 = 5 u	4x5 = 20 u

(a)
Since Zara and Michael gave away the same number of beads, the difference in the number of beads between Zara and Michael 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 5 and 4 is 20.

Michael's beads in February : Michael's beads in March
28 : 5

(b)
Total number of beads in February
= 48 u + 28 u
= 76 u

Total number of beads in March
= 25 u + 5 u
= 30 u

Total beads in February : Total beads in March
76 : 30 _(÷2)
38 : 15 

Answer(s): (a) 28 : 5; (b) 38 : 15