Riordan had some stamps. He gave ²₃ of his stamps to Xavier and bought 4 new stamps. After that, he gave ³₈ of his remaining stamps to his brother and bought another 7 new stamps. In the end, Riordan had 22 stamps.

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

(a)
Fraction of  his remaining stamps after he gave to his brother
= 1 - ³₈
= ⁵₈

⁵₈ of his remaining stamps = 22 - 7 = 15
¹₈ of his remaining stamps = 15 ÷ 5 = 3
³₈ of his remaining stamps = 3 x 3 = 9

Number of stamps that Riordan gave to his brother = 9

(b)
⁸₈ of his remaining stamps = 8 x 3 = 24

Fraction of his total stamps after he gave to Xavier
= 1 - ²₃
= ¹₃

¹₃ of his total stamps = 24 - 4 = 20
³₃ of his total stamps = 3 x 20 = 60

Number of stamps that Riordan had at first = 60 

Answer(s): (a) 9; (b) 60