Kimberly had some brown and yellow balls. If she gives away 40 brown balls, the number of brown balls will be 10% of the total number of balls left. If she gives away 24 yellow balls, the number of brown balls will be 25% of the total number of balls left.

1. How many balls does Kimberly have altogether?
2. What fraction of Kimberly's balls is yellow?

	Scenario 1		Scenario 2
	Brown	Yellow	Brown	Yellow
Before	1 u + 40	9 u	1 p	3 p + 24
Change	- 40	No change	No change	- 24
After	1 u	9 u	1 p	3 p

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

25% = ²⁵₁₀₀ = ¹₄

1 u + 40 = 1 p --- (1)

9 u = 3 p + 24
9 u - 24 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 120 = 3 p --- (3) 

(2) = (3)
9 u - 24 = 3 u + 120 
9 u - 3 u = 120 + 24
6 u = 144

1 u = 144 ÷ 6 = 24

Number of balls that Kimberly had at first
= 1 u + 40 + 9 u
= 10 u + 40
= 10 x 24 + 40
= 240 + 40
= 280

(b)
Number of yellow balls
= 9 u
= 9 x 24
= 216

Fraction of Kimberly's balls that is yellow 
= ²¹⁶₂₈₀
= ²⁷₃₅

Answer(s): (a) 280; (b) ²⁷₃₅