Sean had some beads. He gave ³₄ of his beads to Vincent and bought 4 new beads. After that, he gave ²₅ of his remaining beads to his sister and bought another 7 new beads. In the end, Sean had 28 beads.

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

(a)
Fraction of  his remaining beads after he gave to his sister
= 1 - ²₅
= ³₅

³₅ of his remaining beads = 28 - 7 = 21
¹₅ of his remaining beads = 21 ÷ 3 = 7
²₅ of his remaining beads = 2 x 7 = 14

Number of beads that Sean gave to his sister = 14

(b)
⁵₅ of his remaining beads = 5 x 7 = 35

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

¹₄ of his total beads = 35 - 4 = 31
⁴₄ of his total beads = 4 x 31 = 124

Number of beads that Sean had at first = 124 

Answer(s): (a) 14; (b) 124