PSLE
Fanny had a total of 115 purple and orange beads. She used 25 purple beads and 90% of the orange beads. After that, the ratio of the number of purple beads to orange beads Fanny had was 5 : 1.

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

	Purple beads	Orange beads	Total
Before	5 u + 25	10 u	15 u + 25
Change	- 25	- 9 u
After	5 u	1 u	6 u
Comparing purple beads and orange beads in the end	5	1	6

(a)
90% = ⁹⁰₁₀₀ = ⁹₁₀

Fraction of her orange beads that Fanny used = ⁹₁₀

(b)
The number of orange 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 orange beads at first = 10 u
Number of purple beads at first = 5 u + 25

Total number of beads at first
= 10 u + 5 u + 25
= 15 u + 25

15 u + 25 = 115
15 u = 115 - 25
15 u = 90

1 u = 90 ÷ 15 = 6

Number of orange beads in the end = 1 u
Number of purple beads in the end = 5 u

Total number of beads in the end
= 5 u + 1 u
= 6 u
= 6 x 6
= 36

Answer(s): (a)⁹₁₀; (b) 36