In March, Jade and Sam had buttons in the ratio 14 : 5. In April, each of them gave away the same number of buttons. Jade then had five times as many buttons as Sam.

1. Find the ratio of the number of buttons Sam 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.

	Jade	Sam	Difference
Before	14x4 = 56 u	5x4 = 20 u	9x4 = 36 u
Change	- 11 u	- 11 u
After	5x9 = 45 u	1x9 = 9 u	4x9 = 36 u

(a)
Since Jade and Sam gave away the same number of buttons, the difference in the number of buttons between Jade and Sam 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 9 and 4 is 36.

Sam's buttons in March : Sam's buttons in April
20 : 9

(b)
Total number of buttons in March
= 56 u + 20 u
= 76 u

Total number of buttons in April
= 45 u + 9 u
= 54 u

Total buttons in March : Total buttons in April
76 : 54 _(÷2)
38 : 27 

Answer(s): (a) 20 : 9; (b) 38 : 27