Tim had some stamps. He gave ²₃ of his stamps to Perry and bought 4 new stamps. After that, he gave ⁴₉ of his remaining stamps to his sister and bought another 7 new stamps. In the end, Tim had 42 stamps.

1. How many stamps did Tim give to his sister?
2. How many stamps did Tim have at first?

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

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

Number of stamps that Tim gave to his sister = 28

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

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

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

Number of stamps that Tim had at first = 177 

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