Neave had some erasers. He gave ³₄ of his erasers to Ian and bought 4 new erasers. After that, he gave ³₅ of his remaining erasers to his cousin and bought another 7 new erasers. In the end, Neave had 23 erasers.

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

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

²₅ of his remaining erasers = 23 - 7 = 16
¹₅ of his remaining erasers = 16 ÷ 2 = 8
³₅ of his remaining erasers = 3 x 8 = 24

Number of erasers that Neave gave to his cousin = 24

(b)
⁵₅ of his remaining erasers = 5 x 8 = 40

Fraction of his total erasers after he gave to Ian
= 1 - ³₄
= ¹₄

¹₄ of his total erasers = 40 - 4 = 36
⁴₄ of his total erasers = 4 x 36 = 144

Number of erasers that Neave had at first = 144 

Answer(s): (a) 24; (b) 144