PSLE
Kathy had a total of 271 purple and orange beads. She used 16 purple beads and 70% of the orange beads. After that, the ratio of the number of purple beads to orange beads Kathy had was 7 : 3.

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

	Purple	Orange	Total
Before	7 u + 16	10 u	17 u + 16
Change	- 16	- 7 u
After	7 u	3 u	10 u
Comparing purple beads and orange beads in the end	7	3	10

(a)
70% = ⁷⁰₁₀₀ = ⁷₁₀

Fraction of her orange beads that Kathy used = ⁷₁₀

Fraction of her orange beads that Kathy was left with
= 1 - ⁷₁₀
= ³₁₀

(b)
The number of orange 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 orange beads at first = 10 u
Number of purple beads at first = 7 u + 16

Total number of beads at first
= 10 u + 7 u + 16
= 17 u + 16

17 u + 16 = 271
17 u = 271 - 16
17 u = 255

1 u = 255 ÷ 17 = 15

Number of orange beads in the end = 3 u
Number of purple beads in the end = 7 u

Number of more purple beads than orange beads that Kathy had in the end
= 7 u - 3 u
= 4 u
= 4 x 15
= 60

Answer(s): (a)³₁₀; (b) 60