Peter had some beads. He gave ⁵₆ of his beads to Billy and bought 4 new beads. After that, he gave ⁴₉ of his remaining beads to his cousin and bought another 7 new beads. In the end, Peter had 27 beads.

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

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

⁵₉ of his remaining beads = 27 - 7 = 20
¹₉ of his remaining beads = 20 ÷ 5 = 4
⁴₉ of his remaining beads = 4 x 4 = 16

Number of beads that Peter gave to his cousin = 16

(b)
⁹₉ of his remaining beads = 9 x 4 = 36

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

¹₆ of his total beads = 36 - 4 = 32
⁶₆ of his total beads = 6 x 32 = 192

Number of beads that Peter had at first = 192 

Answer(s): (a) 16; (b) 192