PSLE
Shannon had a total of 161 black and red beads. She used 25 black beads and 70% of the red beads. After that, the ratio of the number of black beads to red beads Shannon had was 7 : 3.

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

	Black	Red	Total
Before	7 u + 25	10 u	17 u + 25
Change	- 25	- 7 u
After	7 u	3 u	10 u
Comparing black beads and red beads in the end	7	3	10

(a)
70% = ⁷⁰₁₀₀ = ⁷₁₀

Fraction of her red beads that Shannon used = ⁷₁₀

Fraction of her red beads that Shannon was left with
= 1 - ⁷₁₀
= ³₁₀

(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 = 10 u
Number of black beads at first = 7 u + 25

Total number of beads at first
= 10 u + 7 u + 25
= 17 u + 25

17 u + 25 = 161
17 u = 161 - 25
17 u = 136

1 u = 136 ÷ 17 = 8

Number of red beads in the end = 3 u
Number of black beads in the end = 7 u

Number of more black beads than red beads that Shannon had in the end
= 7 u - 3 u
= 4 u
= 4 x 8
= 32

Answer(s): (a)³₁₀; (b) 32