PSLE
Sarah had a total of 178 blue and red beads. She used 34 blue beads and 80% of the red beads. After that, the ratio of the number of blue beads to red beads Sarah had was 3 : 1.

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

	Blue	Red	Total
Before	3 u + 34	5 u	8 u + 34
Change	- 34	- 4 u
After	3 u	1 u	4 u
Comparing blue beads and red beads in the end	3	1	4

(a)
80% = ⁸⁰₁₀₀ = ⁴₅

Fraction of her red beads that Sarah used = ⁴₅

Fraction of her red beads that Sarah was left with
= 1 - ⁴₅
= ¹₅

(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 = 5 u
Number of blue beads at first = 3 u + 34

Total number of beads at first
= 5 u + 3 u + 34
= 8 u + 34

8 u + 34 = 178
8 u = 178 - 34
8 u = 144

1 u = 144 ÷ 8 = 18

Number of red beads in the end = 1 u
Number of blue beads in the end = 3 u

Number of more blue beads than red beads that Sarah had in the end
= 3 u - 1 u
= 2 u
= 2 x 18
= 36

Answer(s): (a)¹₅; (b) 36