Liam had some erasers. He gave ⁵₆ of his erasers to Perry and bought 4 new erasers. After that, he gave ³₈ of his remaining erasers to his sister and bought another 7 new erasers. In the end, Liam had 27 erasers.

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

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

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

Number of erasers that Liam gave to his sister = 12

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

Fraction of his total erasers after he gave to Perry
= 1 - ⁵₆
= ¹₆

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

Number of erasers that Liam had at first = 168 

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