Seth had some cards. He gave ²₃ of his cards to Ben and bought 4 new cards. After that, he gave ²₅ of his remaining cards to his brother and bought another 7 new cards. In the end, Seth had 37 cards.

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

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

³₅ of his remaining cards = 37 - 7 = 30
¹₅ of his remaining cards = 30 ÷ 3 = 10
²₅ of his remaining cards = 2 x 10 = 20

Number of cards that Seth gave to his brother = 20

(b)
⁵₅ of his remaining cards = 5 x 10 = 50

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

¹₃ of his total cards = 50 - 4 = 46
³₃ of his total cards = 3 x 46 = 138

Number of cards that Seth had at first = 138 

Answer(s): (a) 20; (b) 138