PSLE
Anna had a total of 82 red and orange beads. She used 22 red beads and 50% of the orange beads. After that, the ratio of the number of red beads to orange beads Anna had was 8 : 1.

1. What fraction of her orange beads was Anna left with? Give your answer in the simplest form.
2. How many more red beads than orange beads did Anna have in the end?

	Red	Orange	Total
Before	8 u + 22	2 u	10 u + 22
Change	- 22	- 1 u
After	8 u	1 u	9 u
Comparing red beads and orange beads in the end	8	1	9

(a)
50% = ⁵⁰₁₀₀ = ¹₂

Fraction of her orange beads that Anna used = ¹₂

Fraction of her orange beads that Anna was left with
= 1 - ¹₂
= ¹₂

(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 = 2 u
Number of red beads at first = 8 u + 22

Total number of beads at first
= 2 u + 8 u + 22
= 10 u + 22

10 u + 22 = 82
10 u = 82 - 22
10 u = 60

1 u = 60 ÷ 10 = 6

Number of orange beads in the end = 1 u
Number of red beads in the end = 8 u

Number of more red beads than orange beads that Anna had in the end
= 8 u - 1 u
= 7 u
= 7 x 6
= 42

Answer(s): (a)¹₂; (b) 42