Jeremy had some erasers. He gave ²₃ of his erasers to Tom and bought 4 new erasers. After that, he gave ²₇ of his remaining erasers to his sister and bought another 7 new erasers. In the end, Jeremy had 37 erasers.

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

(a)
Fraction of  his remaining erasers after he gave to his sister
= 1 - ²₇
= ⁵₇

⁵₇ of his remaining erasers = 37 - 7 = 30
¹₇ of his remaining erasers = 30 ÷ 5 = 6
²₇ of his remaining erasers = 2 x 6 = 12

Number of erasers that Jeremy gave to his sister = 12

(b)
⁷₇ of his remaining erasers = 7 x 6 = 42

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

¹₃ of his total erasers = 42 - 4 = 38
³₃ of his total erasers = 3 x 38 = 114

Number of erasers that Jeremy had at first = 114 

Answer(s): (a) 12; (b) 114