Ken had some erasers. He gave ²₃ of his erasers to Seth and bought 4 new erasers. After that, he gave ⁴₉ of his remaining erasers to his brother and bought another 7 new erasers. In the end, Ken had 42 erasers.

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

(a)
Fraction of  his remaining erasers after he gave to his brother
= 1 - ⁴₉
= ⁵₉

⁵₉ of his remaining erasers = 42 - 7 = 35
¹₉ of his remaining erasers = 35 ÷ 5 = 7
⁴₉ of his remaining erasers = 4 x 7 = 28

Number of erasers that Ken gave to his brother = 28

(b)
⁹₉ of his remaining erasers = 9 x 7 = 63

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

¹₃ of his total erasers = 63 - 4 = 59
³₃ of his total erasers = 3 x 59 = 177

Number of erasers that Ken had at first = 177 

Answer(s): (a) 28; (b) 177