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

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

	Xylia	Tim	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 Xylia and Tim gave away the same number of beads, the difference in the number of beads between Xylia and Tim 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.

Tim's beads in January : Tim's beads in February
28 : 5

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

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

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

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