Pierre had some beads. He gave ³₄ of his beads to Dylan 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, Pierre had 42 beads.

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

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

⁵₇ of his remaining beads = 42 - 7 = 35
¹₇ of his remaining beads = 35 ÷ 5 = 7
²₇ of his remaining beads = 2 x 7 = 14

Number of beads that Pierre gave to his sister = 14

(b)
⁷₇ of his remaining beads = 7 x 7 = 49

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

¹₄ of his total beads = 49 - 4 = 45
⁴₄ of his total beads = 4 x 45 = 180

Number of beads that Pierre had at first = 180 

Answer(s): (a) 14; (b) 180