PSLE
Shannon had a total of 263 purple and pink beads. She used 16 purple beads and 90% of the pink beads. After that, the ratio of the number of purple beads to pink beads Shannon had was 3 : 1.

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

	Purple	Pink	Total
Before	3 u + 16	10 u	13 u + 16
Change	- 16	- 9 u
After	3 u	1 u	4 u
Comparing purple beads and pink beads in the end	3	1	4

(a)
90% = ⁹⁰₁₀₀ = ⁹₁₀

Fraction of her pink beads that Shannon used = ⁹₁₀

Fraction of her pink beads that Shannon was left with
= 1 - ⁹₁₀
= ¹₁₀

(b)
The number of pink 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 pink beads at first = 10 u
Number of purple beads at first = 3 u + 16

Total number of beads at first
= 10 u + 3 u + 16
= 13 u + 16

13 u + 16 = 263
13 u = 263 - 16
13 u = 247

1 u = 247 ÷ 13 = 19

Number of pink beads in the end = 1 u
Number of purple beads in the end = 3 u

Number of more purple beads than pink beads that Shannon had in the end
= 3 u - 1 u
= 2 u
= 2 x 19
= 38

Answer(s): (a)¹₁₀; (b) 38