Asher, Gabriel and Andy had some beads in the ratio of 6 : 7 : 13. Andy gave 40% of his beads to Asher and Gabriel. As a result, Asher had the same number of beads as Gabriel and Andy had 39 fewer beads than Asher.

1. What was the percentage increase in Asher's beads after receiving from Andy?
2. How many beads did Gabriel have at first?

Asher	Gabriel	Andy	Total
6 u	7 u	13 u	26 u
+ 5.2 u		- 5.2 u
9.1 u	9.1 u	7.8 u	26 u

(a)
Number of beads that Andy gave away
= 40% x 13
= ⁴⁰₁₀₀ x 13
= 5.2 u

Number of beads that Asher and Gabriel each had in the end
= (26 u - 7.8 u) ÷ 2
= 18.2 u ÷ 2
= 9.1 u

Increase in the number of beads that Asher had
= 9.1 u - 6 u
= 3.1 u

Percentage increase in Asher's beads after receiving from Andy
= ^3.1₆ x 100%
= 51.666666666667%

(b)
9.1 u = 7.8 u + 39
9.1 u - 7.8 u = 39
1.3 u = 39

1 u = 39 ÷ 1.3 = 30

Number of beads that Gabriel had at first
= 7 u
= 7 x 30
= 210

Answer(s): (a) 51.666666666667%; (b) 210