Wendy had some red and gold marbles. If she gives away 26 red marbles, the number of red marbles will be 10% of the total number of marbles left. If she gives away 36 gold marbles, the number of red marbles will be 25% of the total number of marbles left.

1. How many marbles does Wendy have altogether?
2. What fraction of Wendy's marbles is gold?

	Scenario 1		Scenario 2
	Red	Gold	Red	Gold
Before	1 u + 26	9 u	1 p	3 p + 36
Change	- 26	No change	No change	- 36
After	1 u	9 u	1 p	3 p

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

25% = ²⁵₁₀₀ = ¹₄

1 u + 26 = 1 p --- (1)

9 u = 3 p + 36
9 u - 36 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 78 = 3 p --- (3) 

(2) = (3)
9 u - 36 = 3 u + 78 
9 u - 3 u = 78 + 36
6 u = 114

1 u = 114 ÷ 6 = 19

Number of marbles that Wendy had at first
= 1 u + 26 + 9 u
= 10 u + 26
= 10 x 19 + 26
= 190 + 26
= 216

(b)
Number of gold marbles
= 9 u
= 9 x 19
= 171

Fraction of Wendy's marbles that is gold 
= ¹⁷¹₂₁₆
= ¹⁹₂₄

Answer(s): (a) 216; (b) ¹⁹₂₄