Liam had some cards. He gave ⁶₇ of his cards to Xavier and bought 4 new cards. After that, he gave ⁴₉ of his remaining cards to his sister and bought another 7 new cards. In the end, Liam had 22 cards.

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

(a)
Fraction of  his remaining cards after he gave to his sister
= 1 - ⁴₉
= ⁵₉

⁵₉ of his remaining cards = 22 - 7 = 15
¹₉ of his remaining cards = 15 ÷ 5 = 3
⁴₉ of his remaining cards = 4 x 3 = 12

Number of cards that Liam gave to his sister = 12

(b)
⁹₉ of his remaining cards = 9 x 3 = 27

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

¹₇ of his total cards = 27 - 4 = 23
⁷₇ of his total cards = 7 x 23 = 161

Number of cards that Liam had at first = 161 

Answer(s): (a) 12; (b) 161