Shiyun had some yellow and white beads. If she gives away 44 yellow beads, the number of yellow beads will be 10% of the total number of beads left. If she gives away 36 white beads, the number of yellow beads will be 25% of the total number of beads left.

1. How many beads does Shiyun have altogether?
2. What fraction of Shiyun's beads is white?

	Scenario 1		Scenario 2
	Yellow	White	Yellow	White
Before	1 u + 44	9 u	1 p	3 p + 36
Change	- 44	No change	No change	- 36
After	1 u	9 u	1 p	3 p

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

25% = ²⁵₁₀₀ = ¹₄

1 u + 44 = 1 p --- (1)

9 u = 3 p + 36
9 u - 36 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 132 = 3 p --- (3) 

(2) = (3)
9 u - 36 = 3 u + 132 
9 u - 3 u = 132 + 36
6 u = 168

1 u = 168 ÷ 6 = 28

Number of beads that Shiyun had at first
= 1 u + 44 + 9 u
= 10 u + 44
= 10 x 28 + 44
= 280 + 44
= 324

(b)
Number of white beads
= 9 u
= 9 x 28
= 252

Fraction of Shiyun's beads that is white 
= ²⁵²₃₂₄
= ⁷₉

Answer(s): (a) 324; (b) ⁷₉