Tom had some beads. He gave ²₃ of his beads to Elijah and bought 4 new beads. After that, he gave ⁵₈ of his remaining beads to his brother and bought another 7 new beads. In the end, Tom had 25 beads.

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

(a)
Fraction of  his remaining beads after he gave to his brother
= 1 - ⁵₈
= ³₈

³₈ of his remaining beads = 25 - 7 = 18
¹₈ of his remaining beads = 18 ÷ 3 = 6
⁵₈ of his remaining beads = 5 x 6 = 30

Number of beads that Tom gave to his brother = 30

(b)
⁸₈ of his remaining beads = 8 x 6 = 48

Fraction of his total beads after he gave to Elijah
= 1 - ²₃
= ¹₃

¹₃ of his total beads = 48 - 4 = 44
³₃ of his total beads = 3 x 44 = 132

Number of beads that Tom had at first = 132 

Answer(s): (a) 30; (b) 132