George had some beads. He gave ⁵₆ of his beads to Howard 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, George had 32 beads.

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

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

⁵₇ of his remaining beads = 32 - 7 = 25
¹₇ of his remaining beads = 25 ÷ 5 = 5
²₇ of his remaining beads = 2 x 5 = 10

Number of beads that George gave to his brother = 10

(b)
⁷₇ of his remaining beads = 7 x 5 = 35

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

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

Number of beads that George had at first = 186 

Answer(s): (a) 10; (b) 186