Paul had some cards. He gave ³₄ of his cards to Vaidev and bought 4 new cards. After that, he gave ³₈ of his remaining cards to his brother and bought another 7 new cards. In the end, Paul had 37 cards.

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

(a)
Fraction of  his remaining cards after he gave to his brother
= 1 - ³₈
= ⁵₈

⁵₈ of his remaining cards = 37 - 7 = 30
¹₈ of his remaining cards = 30 ÷ 5 = 6
³₈ of his remaining cards = 3 x 6 = 18

Number of cards that Paul gave to his brother = 18

(b)
⁸₈ of his remaining cards = 8 x 6 = 48

Fraction of his total cards after he gave to Vaidev
= 1 - ³₄
= ¹₄

¹₄ of his total cards = 48 - 4 = 44
⁴₄ of his total cards = 4 x 44 = 176

Number of cards that Paul had at first = 176 

Answer(s): (a) 18; (b) 176