Xavier had some beads. He gave ⁵₆ of his beads to Gabriel and bought 4 new beads. After that, he gave ³₅ of his remaining beads to his brother and bought another 7 new beads. In the end, Xavier had 21 beads.

1. How many beads did Xavier give to his brother?
2. How many beads did Xavier have at first?

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

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

Number of beads that Xavier gave to his brother = 21

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

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

¹₆ of his total beads = 35 - 4 = 31
⁶₆ of his total beads = 6 x 31 = 186

Number of beads that Xavier had at first = 186 

Answer(s): (a) 21; (b) 186