PSLE
Hilda had a total of 99 orange and purple beads. She used 24 orange beads and 90% of the purple beads. After that, the ratio of the number of orange beads to purple beads Hilda had was 5 : 1.

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

	Orange	Purple	Total
Before	5 u + 24	10 u	15 u + 24
Change	- 24	- 9 u
After	5 u	1 u	6 u
Comparing orange beads and purple beads in the end	5	1	6

(a)
90% = ⁹⁰₁₀₀ = ⁹₁₀

Fraction of her purple beads that Hilda used = ⁹₁₀

Fraction of her purple beads that Hilda was left with
= 1 - ⁹₁₀
= ¹₁₀

(b)
The number of purple 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 purple beads at first = 10 u
Number of orange beads at first = 5 u + 24

Total number of beads at first
= 10 u + 5 u + 24
= 15 u + 24

15 u + 24 = 99
15 u = 99 - 24
15 u = 75

1 u = 75 ÷ 15 = 5

Number of purple beads in the end = 1 u
Number of orange beads in the end = 5 u

Number of more orange beads than purple beads that Hilda had in the end
= 5 u - 1 u
= 4 u
= 4 x 5
= 20

Answer(s): (a)¹₁₀; (b) 20