Justin, Jenson and Japheth had some cards in the ratio of 5 : 6 : 11. Japheth gave 50% of his cards to Justin and Jenson. As a result, Justin had the same number of cards as Jenson and Japheth had 33 fewer cards than Justin.

1. What was the percentage increase in Justin's cards after receiving from Japheth?
2. How many cards did Jenson have at first?

Justin	Jenson	Japheth	Total
5 u	6 u	11 u	22 u
+ 5.5 u		- 5.5 u
8.25 u	8.25 u	5.5 u	22 u

(a)
Number of cards that Japheth gave away
= 50% x 11
= ⁵⁰₁₀₀ x 11
= 5.5 u

Number of cards that Justin and Jenson each had in the end
= (22 u - 5.5 u) ÷ 2
= 16.5 u ÷ 2
= 8.25 u

Increase in the number of cards that Justin had
= 8.25 u - 5 u
= 3.25 u

Percentage increase in Justin's cards after receiving from Japheth
= ^3.25₅ x 100%
= 65%

(b)
8.25 u = 5.5 u + 33
8.25 u - 5.5 u = 33
2.75 u = 33

1 u = 33 ÷ 2.75 = 12

Number of cards that Jenson had at first
= 6 u
= 6 x 12
= 72

Answer(s): (a) 65%; (b) 72