Ben had some cards. He gave ²₃ of his cards to Brandon 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, Ben had 42 cards.

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

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

⁵₈ of his remaining cards = 42 - 7 = 35
¹₈ of his remaining cards = 35 ÷ 5 = 7
³₈ of his remaining cards = 3 x 7 = 21

Number of cards that Ben gave to his brother = 21

(b)
⁸₈ of his remaining cards = 8 x 7 = 56

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

¹₃ of his total cards = 56 - 4 = 52
³₃ of his total cards = 3 x 52 = 156

Number of cards that Ben had at first = 156 

Answer(s): (a) 21; (b) 156