PSLE
Xuan had a total of 130 blue and black beads. She used 50 blue beads and 40% of the black beads. After that, the ratio of the number of blue beads to black beads Xuan had was 5 : 3.

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

	Blue	Black	Total
Before	5 u + 50	5 u	10 u + 50
Change	- 50	- 2 u
After	5 u	3 u	8 u
Comparing blue beads and black beads in the end	5	3	8

(a)
40% = ⁴⁰₁₀₀ = ²₅

Fraction of her black beads that Xuan used = ²₅

Fraction of her black beads that Xuan was left with
= 1 - ²₅
= ³₅

(b)
The number of black 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 black beads at first = 5 u
Number of blue beads at first = 5 u + 50

Total number of beads at first
= 5 u + 5 u + 50
= 10 u + 50

10 u + 50 = 130
10 u = 130 - 50
10 u = 80

1 u = 80 ÷ 10 = 8

Number of black beads in the end = 3 u
Number of blue beads in the end = 5 u

Number of more blue beads than black beads that Xuan had in the end
= 5 u - 3 u
= 2 u
= 2 x 8
= 16

Answer(s): (a)³₅; (b) 16