Reggie had some beads. He gave ⁷₈ of his beads to Dylan and bought 4 new beads. After that, he gave ²₇ of his remaining beads to his brother and bought another 7 new beads. In the end, Reggie had 27 beads.

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

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

⁵₇ of his remaining beads = 27 - 7 = 20
¹₇ of his remaining beads = 20 ÷ 5 = 4
²₇ of his remaining beads = 2 x 4 = 8

Number of beads that Reggie gave to his brother = 8

(b)
⁷₇ of his remaining beads = 7 x 4 = 28

Fraction of his total beads after he gave to Dylan
= 1 - ⁷₈
= ¹₈

¹₈ of his total beads = 28 - 4 = 24
⁸₈ of his total beads = 8 x 24 = 192

Number of beads that Reggie had at first = 192 

Answer(s): (a) 8; (b) 192