Ivan had some beads. He gave ⁵₆ of his beads to Jeremy 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, Ivan had 25 beads.

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

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

³₅ of his remaining beads = 25 - 7 = 18
¹₅ of his remaining beads = 18 ÷ 3 = 6
²₅ of his remaining beads = 2 x 6 = 12

Number of beads that Ivan gave to his brother = 12

(b)
⁵₅ of his remaining beads = 5 x 6 = 30

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

¹₆ of his total beads = 30 - 4 = 26
⁶₆ of his total beads = 6 x 26 = 156

Number of beads that Ivan had at first = 156 

Answer(s): (a) 12; (b) 156