Will had some cards. He gave ²₃ of his cards to Asher and bought 4 new cards. After that, he gave ³₅ of his remaining cards to his brother and bought another 7 new cards. In the end, Will had 35 cards.

1. How many cards did Will give to his brother?
2. How many cards did Will have at first?

(a)
Fraction of  his remaining cards after he gave to his brother
= 1 - ³₅
= ²₅

²₅ of his remaining cards = 35 - 7 = 28
¹₅ of his remaining cards = 28 ÷ 2 = 14
³₅ of his remaining cards = 3 x 14 = 42

Number of cards that Will gave to his brother = 42

(b)
⁵₅ of his remaining cards = 5 x 14 = 70

Fraction of his total cards after he gave to Asher
= 1 - ²₃
= ¹₃

¹₃ of his total cards = 70 - 4 = 66
³₃ of his total cards = 3 x 66 = 198

Number of cards that Will had at first = 198 

Answer(s): (a) 42; (b) 198