Luke had some cards. He gave ⁵₆ of his cards to Mark 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, Luke had 27 cards.

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

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

⁵₈ of his remaining cards = 27 - 7 = 20
¹₈ of his remaining cards = 20 ÷ 5 = 4
³₈ of his remaining cards = 3 x 4 = 12

Number of cards that Luke gave to his brother = 12

(b)
⁸₈ of his remaining cards = 8 x 4 = 32

Fraction of his total cards after he gave to Mark
= 1 - ⁵₆
= ¹₆

¹₆ of his total cards = 32 - 4 = 28
⁶₆ of his total cards = 6 x 28 = 168

Number of cards that Luke had at first = 168 

Answer(s): (a) 12; (b) 168