PSLE
Xylia had a total of 191 purple and red beads. She used 48 purple beads and 10% of the red beads. After that, the ratio of the number of purple beads to red beads Xylia had was 1 : 9.

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

	Purple beads	Red beads	Total
Before	1 u + 48	10 u	11 u + 48
Change	- 48	- 1 u
After	1 u	9 u	10 u
Comparing purple beads and red beads in the end	1	9	10

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

Fraction of her red beads that Xylia used = ¹₁₀

(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 purple beads at first = 1 u + 48

Total number of beads at first
= 10 u + 1 u + 48
= 11 u + 48

11 u + 48 = 191
11 u = 191 - 48
11 u = 143

1 u = 143 ÷ 11 = 13

Number of red beads in the end = 9 u
Number of purple beads in the end = 1 u

Total number of beads in the end
= 1 u + 9 u
= 10 u
= 10 x 13
= 130

Answer(s): (a)¹₁₀; (b) 130