PSLE
Zoe had a total of 90 black and blue beads. She used 10 black beads and 75% of the blue beads. After that, the ratio of the number of black beads to blue beads Zoe had was 4 : 1.

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

	Black	Blue	Total
Before	4 u + 10	4 u	8 u + 10
Change	- 10	- 3 u
After	4 u	1 u	5 u
Comparing black beads and blue beads in the end	4	1	5

(a)
75% = ⁷⁵₁₀₀ = ³₄

Fraction of her blue beads that Zoe used = ³₄

Fraction of her blue beads that Zoe 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 black beads at first = 4 u + 10

Total number of beads at first
= 4 u + 4 u + 10
= 8 u + 10

8 u + 10 = 90
8 u = 90 - 10
8 u = 80

1 u = 80 ÷ 8 = 10

Number of blue beads in the end = 1 u
Number of black beads in the end = 4 u

Number of more black beads than blue beads that Zoe had in the end
= 4 u - 1 u
= 3 u
= 3 x 10
= 30

Answer(s): (a)¹₄; (b) 30