Howard had some beads. He gave ²₃ of his beads to Paul 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, Howard had 27 beads.

1. How many beads did Howard give to his cousin?
2. How many beads did Howard 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 Howard gave to his cousin = 16

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

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

¹₃ of his total beads = 36 - 4 = 32
³₃ of his total beads = 3 x 32 = 96

Number of beads that Howard had at first = 96 

Answer(s): (a) 16; (b) 96