Reggie had some erasers. He gave ²₃ of his erasers to Ben and bought 4 new erasers. After that, he gave ²₇ of his remaining erasers to his brother and bought another 7 new erasers. In the end, Reggie had 42 erasers.

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

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

⁵₇ of his remaining erasers = 42 - 7 = 35
¹₇ of his remaining erasers = 35 ÷ 5 = 7
²₇ of his remaining erasers = 2 x 7 = 14

Number of erasers that Reggie gave to his brother = 14

(b)
⁷₇ of his remaining erasers = 7 x 7 = 49

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

¹₃ of his total erasers = 49 - 4 = 45
³₃ of his total erasers = 3 x 45 = 135

Number of erasers that Reggie had at first = 135 

Answer(s): (a) 14; (b) 135