In March, Marion and Tim had buttons in the ratio 7 : 4. In April, each of them gave away the same number of buttons. Marion then had five times as many buttons as Tim.

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

	Marion	Tim	Difference
Before	7x4 = 28 u	4x4 = 16 u	3x4 = 12 u
Change	- 13 u	- 13 u
After	5x3 = 15 u	1x3 = 3 u	4x3 = 12 u

(a)
Since Marion and Tim gave away the same number of buttons, the difference in the number of buttons between Marion and Tim at first and in the end remains the same.

Make the difference in the number of buttons at first and in the end the same. LCM of 3 and 4 is 12.

Tim's buttons in March : Tim's buttons in April
16 : 3

(b)
Total number of buttons in March
= 28 u + 16 u
= 44 u

Total number of buttons in April
= 15 u + 3 u
= 18 u

Total buttons in March : Total buttons in April
44 : 18 _(÷2)
22 : 9 

Answer(s): (a) 16 : 3; (b) 22 : 9