Pamela and Ken collect cards and beads. Ken has 40 less cards than beads. Ken has 5 times the number of cards Pamela has, and Pamela has 30% more beads than Ken. After Pamela gives Ken all of her cards and Ken gives Pamela 70% of his beads, Ken has 33 more cards than beads. Find the number of beads Pamela has at first.

Pamela		Ken
Beads	Cards	Beads	Cards
6.5 u + 52	1 u	5 u + 40	5 u
+ 3.5 u + 28	- 1 u	- 3.5 u - 28	+ 1 u
10 u + 80	0	1.5 u + 12	6 u

100%+ 30% = 130% 

130% x 5 u
= ¹³⁰₁₀₀ x 5 u
= 6.5 u

130% x 40
= ¹³⁰₁₀₀ x 40
= 52 

70% x 5 u
= ⁷⁰₁₀₀ x 5 u
= 3.5 u  

70% x 40 
= ⁷⁰₁₀₀ x 40
= 28 

If another 33 beads are given to Ken, he will have equal number of beads and cards in the end.
6 u = 1.5 u + 12 + 33
6 u - 1.5 u = 45
4.5 u = 45

1 u = 45 ÷ 4.5 = 10

Number of beads that Pamela has at first
= 6.5 u + 52
= 6.5 x 10 + 52
= 65 + 52
= 117
 
Answer(s): 117