PSLE
Sarah had a total of 114 yellow and blue beads. She used 23 yellow beads and 75% of the blue beads. After that, the ratio of the number of yellow beads to blue beads Sarah had was 9 : 1.

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

	Yellow	Blue	Total
Before	9 u + 23	4 u	13 u + 23
Change	- 23	- 3 u
After	9 u	1 u	10 u
Comparing yellow beads and blue beads in the end	9	1	10

(a)
75% = ⁷⁵₁₀₀ = ³₄

Fraction of her blue beads that Sarah used = ³₄

Fraction of her blue beads that Sarah was left with
= 1 - ³₄
= ¹₄

(b)
The number of blue 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 blue beads at first = 4 u
Number of yellow beads at first = 9 u + 23

Total number of beads at first
= 4 u + 9 u + 23
= 13 u + 23

13 u + 23 = 114
13 u = 114 - 23
13 u = 91

1 u = 91 ÷ 13 = 7

Number of blue beads in the end = 1 u
Number of yellow beads in the end = 9 u

Number of more yellow beads than blue beads that Sarah had in the end
= 9 u - 1 u
= 8 u
= 8 x 7
= 56

Answer(s): (a)¹₄; (b) 56