Nick had some beads. He gave ⁵₆ of his beads to Rael and bought 4 new beads. After that, he gave ²₇ of his remaining beads to his cousin and bought another 7 new beads. In the end, Nick had 32 beads.

1. How many beads did Nick give to his cousin?
2. How many beads did Nick have at first?

(a)
Fraction of  his remaining beads after he gave to his cousin
= 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 Nick gave to his cousin = 10

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

Fraction of his total beads after he gave to Rael
= 1 - ⁵₆
= ¹₆

¹₆ of his total beads = 35 - 4 = 31
⁶₆ of his total beads = 6 x 31 = 186

Number of beads that Nick had at first = 186 

Answer(s): (a) 10; (b) 186