PSLE
Diana had a total of 83 purple and orange beads. She used 11 purple beads and 20% of the orange beads. After that, the ratio of the number of purple beads to orange beads Diana had was 1 : 4.

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

	Purple beads	Orange beads	Total
Before	1 u + 11	5 u	6 u + 11
Change	- 11	- 1 u
After	1 u	4 u	5 u
Comparing purple beads and orange beads in the end	1	4	5

(a)
20% = ²⁰₁₀₀ = ¹₅

Fraction of her orange beads that Diana used = ¹₅

(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 = 5 u
Number of purple beads at first = 1 u + 11

Total number of beads at first
= 5 u + 1 u + 11
= 6 u + 11

6 u + 11 = 83
6 u = 83 - 11
6 u = 72

1 u = 72 ÷ 6 = 12

Number of orange beads in the end = 4 u
Number of purple beads in the end = 1 u

Total number of beads in the end
= 1 u + 4 u
= 5 u
= 5 x 12
= 60

Answer(s): (a)¹₅; (b) 60