Crate M contains 9 purple balls and 8 gold balls. Crate N contains 93 purple balls and 42 gold balls. How many gold balls and purple balls must be transferred from Crate N to put into Crate M so that 50% of the balls in Crate A are purple and 70% of the balls in Crate N are purple?

	Crate M		Crate N
	Purple balls	Gold balls	Purple balls	Gold balls
Before	9	8	93	42
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	7 p	3 p

50% = ⁵⁰₁₀₀ = 12

70% = ⁷⁰₁₀₀ = 710

Number of purple balls = 9 + 93 = 102 

Number of gold balls = 8 + 42 = 50 

1 u + 7 p = 102 --- (1)

1 u + 3 p = 50 ---(2)

(1) - (2)
(1 u + 7 p) - (1 u + 3 p) = 102 - 50
7 p - 3 p = 52
4 p = 52

1 p = 52 ÷ 4 = 13

From (2):
1 u + 3 p = 50
1 u + 3 x 13 = 50
1 u + 39 = 50

1 u = 50 - 39 = 11

Number of gold balls to be transferred from Crate N to Crate M
= 42 - 3 p
= 42 - 3 x 13
= 42 - 39
= 3

Number of purple balls to be transferred from Crate N to Crate M
= 1 u - 9
= 11 - 9
= 2

Total number of gold and purple balls to be transferred from Crate N to Crate M
= 3 + 2
= 5

Answer(s): 5