Tommy had some cards. He gave ²₃ of his cards to Tim and bought 4 new cards. After that, he gave ⁵₈ of his remaining cards to his sister and bought another 7 new cards. In the end, Tommy had 28 cards.

1. How many cards did Tommy give to his sister?
2. How many cards did Tommy have at first?

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

³₈ of his remaining cards = 28 - 7 = 21
¹₈ of his remaining cards = 21 ÷ 3 = 7
⁵₈ of his remaining cards = 5 x 7 = 35

Number of cards that Tommy gave to his sister = 35

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

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

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

Number of cards that Tommy had at first = 156 

Answer(s): (a) 35; (b) 156