Michael had some cards. He gave ⁶₇ of his cards to Oliver and bought 4 new cards. After that, he gave ³₈ of his remaining cards to his sister and bought another 7 new cards. In the end, Michael had 22 cards.

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

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

⁵₈ of his remaining cards = 22 - 7 = 15
¹₈ of his remaining cards = 15 ÷ 5 = 3
³₈ of his remaining cards = 3 x 3 = 9

Number of cards that Michael gave to his sister = 9

(b)
⁸₈ of his remaining cards = 8 x 3 = 24

Fraction of his total cards after he gave to Oliver
= 1 - ⁶₇
= ¹₇

¹₇ of his total cards = 24 - 4 = 20
⁷₇ of his total cards = 7 x 20 = 140

Number of cards that Michael had at first = 140 

Answer(s): (a) 9; (b) 140