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

1. How many erasers did Ian give to his cousin?
2. How many erasers did Ian have at first?

(a)
Fraction of  his remaining erasers after he gave to his cousin
= 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 Ian gave to his cousin = 9

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

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

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

Number of erasers that Ian had at first = 60 

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