PSLE
Opal had a total of 237 purple and orange beads. She used 42 purple beads and 70% of the orange beads. After that, the ratio of the number of purple beads to orange beads Opal had was 5 : 3.

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

	Purple beads	Orange beads	Total
Before	5 u + 42	10 u	15 u + 42
Change	- 42	- 7 u
After	5 u	3 u	8 u
Comparing purple beads and orange beads in the end	5	3	8

(a)
70% = ⁷⁰₁₀₀ = ⁷₁₀

Fraction of her orange beads that Opal used = ⁷₁₀

(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 + 42

Total number of beads at first
= 10 u + 5 u + 42
= 15 u + 42

15 u + 42 = 237
15 u = 237 - 42
15 u = 195

1 u = 195 ÷ 15 = 13

Number of orange beads in the end = 3 u
Number of purple beads in the end = 5 u

Total number of beads in the end
= 5 u + 3 u
= 8 u
= 8 x 13
= 104

Answer(s): (a)⁷₁₀; (b) 104