Valen had some stamps. He gave ³₄ of his stamps to Zane and bought 4 new stamps. After that, he gave ⁵₉ of his remaining stamps to his brother and bought another 7 new stamps. In the end, Valen had 27 stamps.

1. How many stamps did Valen give to his brother?
2. How many stamps did Valen have at first?

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

⁴₉ of his remaining stamps = 27 - 7 = 20
¹₉ of his remaining stamps = 20 ÷ 4 = 5
⁵₉ of his remaining stamps = 5 x 5 = 25

Number of stamps that Valen gave to his brother = 25

(b)
⁹₉ of his remaining stamps = 9 x 5 = 45

Fraction of his total stamps after he gave to Zane
= 1 - ³₄
= ¹₄

¹₄ of his total stamps = 45 - 4 = 41
⁴₄ of his total stamps = 4 x 41 = 164

Number of stamps that Valen had at first = 164 

Answer(s): (a) 25; (b) 164