PSLE
Erika had a total of 209 silver and red beads. She used 29 silver beads and 90% of the red beads. After that, the ratio of the number of silver beads to red beads Erika had was 2 : 1.

1. What fraction of her red beads did Erika use? Give your answer in the simplest form.
2. How many beads did Erika have in the end?

	Silver beads	Red beads	Total
Before	2 u + 29	10 u	12 u + 29
Change	- 29	- 9 u
After	2 u	1 u	3 u
Comparing silver beads and red beads in the end	2	1	3

(a)
90% = ⁹⁰₁₀₀ = ⁹₁₀

Fraction of her red beads that Erika used = ⁹₁₀

(b)
The number of red beads in the end is repeated.
Since the numbers are already the same, we do not need to use LCM to make them the same.

Number of red beads at first = 10 u
Number of silver beads at first = 2 u + 29

Total number of beads at first
= 10 u + 2 u + 29
= 12 u + 29

12 u + 29 = 209
12 u = 209 - 29
12 u = 180

1 u = 180 ÷ 12 = 15

Number of red beads in the end = 1 u
Number of silver beads in the end = 2 u

Total number of beads in the end
= 2 u + 1 u
= 3 u
= 3 x 15
= 45

Answer(s): (a)⁹₁₀; (b) 45