Albert had some erasers. He gave ²₃ of his erasers to Justin and bought 4 new erasers. After that, he gave ³₅ of his remaining erasers to his brother and bought another 7 new erasers. In the end, Albert had 31 erasers.

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

(a)
Fraction of  his remaining erasers after he gave to his brother
= 1 - ³₅
= ²₅

²₅ of his remaining erasers = 31 - 7 = 24
¹₅ of his remaining erasers = 24 ÷ 2 = 12
³₅ of his remaining erasers = 3 x 12 = 36

Number of erasers that Albert gave to his brother = 36

(b)
⁵₅ of his remaining erasers = 5 x 12 = 60

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

¹₃ of his total erasers = 60 - 4 = 56
³₃ of his total erasers = 3 x 56 = 168

Number of erasers that Albert had at first = 168 

Answer(s): (a) 36; (b) 168