Luke had some erasers. He gave ²₃ of his erasers to Sam and bought 4 new erasers. After that, he gave ³₈ of his remaining erasers to his brother and bought another 7 new erasers. In the end, Luke had 22 erasers.

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

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

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

Number of erasers that Luke gave to his brother = 9

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

Fraction of his total erasers after he gave to Sam
= 1 - ²₃
= ¹₃

¹₃ of his total erasers = 24 - 4 = 20
³₃ of his total erasers = 3 x 20 = 60

Number of erasers that Luke had at first = 60 

Answer(s): (a) 9; (b) 60