Pierre had some beads. He gave ³₄ of his beads to Lee 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, Pierre had 37 beads.

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

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

⁵₇ of his remaining beads = 37 - 7 = 30
¹₇ of his remaining beads = 30 ÷ 5 = 6
²₇ of his remaining beads = 2 x 6 = 12

Number of beads that Pierre gave to his cousin = 12

(b)
⁷₇ of his remaining beads = 7 x 6 = 42

Fraction of his total beads after he gave to Lee
= 1 - ³₄
= ¹₄

¹₄ of his total beads = 42 - 4 = 38
⁴₄ of his total beads = 4 x 38 = 152

Number of beads that Pierre had at first = 152 

Answer(s): (a) 12; (b) 152