Ryan had some beads. He gave ²₃ of his beads to Albert and bought 4 new beads. After that, he gave ²₇ of his remaining beads to his sister and bought another 7 new beads. In the end, Ryan had 32 beads.

1. How many beads did Ryan give to his sister?
2. How many beads did Ryan have at first?

(a)
Fraction of  his remaining beads after he gave to his sister
= 1 - ²₇
= ⁵₇

⁵₇ of his remaining beads = 32 - 7 = 25
¹₇ of his remaining beads = 25 ÷ 5 = 5
²₇ of his remaining beads = 2 x 5 = 10

Number of beads that Ryan gave to his sister = 10

(b)
⁷₇ of his remaining beads = 7 x 5 = 35

Fraction of his total beads after he gave to Albert
= 1 - ²₃
= ¹₃

¹₃ of his total beads = 35 - 4 = 31
³₃ of his total beads = 3 x 31 = 93

Number of beads that Ryan had at first = 93 

Answer(s): (a) 10; (b) 93