Jeremy, Howard and Sam had some cards in the ratio of 2 : 3 : 5. Sam gave 40% of his cards to Jeremy and Howard. As a result, Jeremy had the same number of cards as Howard and Sam had 19 fewer cards than Jeremy.

1. What was the percentage increase in Jeremy's cards after receiving from Sam?
2. How many cards did Howard have at first?

Jeremy	Howard	Sam	Total
2 u	3 u	5 u	10 u
+ 2 u		- 2 u
3.5 u	3.5 u	3 u	10 u

(a)
Number of cards that Sam gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

Number of cards that Jeremy and Howard each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u

Increase in the number of cards that Jeremy had
= 3.5 u - 2 u
= 1.5 u

Percentage increase in Jeremy's cards after receiving from Sam
= ^1.5₂ x 100%
= 75%

(b)
3.5 u = 3 u + 19
3.5 u - 3 u = 19
0.5 u = 19

1 u = 19 ÷ 0.5 = 38

Number of cards that Howard had at first
= 3 u
= 3 x 38
= 114

Answer(s): (a) 75%; (b) 114