Julian had some erasers. He gave ⁷₈ of his erasers to Caden and bought 4 new erasers. After that, he gave ²₇ of his remaining erasers to his cousin and bought another 7 new erasers. In the end, Julian had 27 erasers.

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

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

⁵₇ of his remaining erasers = 27 - 7 = 20
¹₇ of his remaining erasers = 20 ÷ 5 = 4
²₇ of his remaining erasers = 2 x 4 = 8

Number of erasers that Julian gave to his cousin = 8

(b)
⁷₇ of his remaining erasers = 7 x 4 = 28

Fraction of his total erasers after he gave to Caden
= 1 - ⁷₈
= ¹₈

¹₈ of his total erasers = 28 - 4 = 24
⁸₈ of his total erasers = 8 x 24 = 192

Number of erasers that Julian had at first = 192 

Answer(s): (a) 8; (b) 192