PSLE
Jade had a total of 134 orange and purple beads. She used 15 orange beads and 90% of the purple beads. After that, the ratio of the number of orange beads to purple beads Jade had was 7 : 1.

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

	Orange	Purple	Total
Before	7 u + 15	10 u	17 u + 15
Change	- 15	- 9 u
After	7 u	1 u	8 u
Comparing orange beads and purple beads in the end	7	1	8

(a)
90% = ⁹⁰₁₀₀ = ⁹₁₀

Fraction of her purple beads that Jade used = ⁹₁₀

Fraction of her purple beads that Jade 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 = 7 u + 15

Total number of beads at first
= 10 u + 7 u + 15
= 17 u + 15

17 u + 15 = 134
17 u = 134 - 15
17 u = 119

1 u = 119 ÷ 17 = 7

Number of purple beads in the end = 1 u
Number of orange beads in the end = 7 u

Number of more orange beads than purple beads that Jade had in the end
= 7 u - 1 u
= 6 u
= 6 x 7
= 42

Answer(s): (a)¹₁₀; (b) 42