In February, Marion and Jenson had buttons in the ratio 7 : 5. In March, each of them gave away the same number of buttons. Marion then had five times as many buttons as Jenson.

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

	Marion	Jenson	Difference
Before	7x2 = 14 u	5x2 = 10 u	2x2 = 4 u
Change	- 9 u	- 9 u
After	5x1 = 5 u	1x1 = 1 u	4x1 = 4 u

(a)
Since Marion and Jenson gave away the same number of buttons, the difference in the number of buttons between Marion and Jenson 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 2 and 4 is 4.

Jenson's buttons in February : Jenson's buttons in March
10 : 1

(b)
Total number of buttons in February
= 14 u + 10 u
= 24 u

Total number of buttons in March
= 5 u + 1 u
= 6 u

Total buttons in February : Total buttons in March
24 : 6 _(÷6)
4 : 1 

Answer(s): (a) 10 : 1; (b) 4 : 1