Bobby had some beads. He gave ³₄ of his beads to Gabriel and bought 4 new beads. After that, he gave ²₅ of his remaining beads to his brother and bought another 7 new beads. In the end, Bobby had 31 beads.

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

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

³₅ of his remaining beads = 31 - 7 = 24
¹₅ of his remaining beads = 24 ÷ 3 = 8
²₅ of his remaining beads = 2 x 8 = 16

Number of beads that Bobby gave to his brother = 16

(b)
⁵₅ of his remaining beads = 5 x 8 = 40

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

¹₄ of his total beads = 40 - 4 = 36
⁴₄ of his total beads = 4 x 36 = 144

Number of beads that Bobby had at first = 144 

Answer(s): (a) 16; (b) 144