PSLE
Marion had a total of 163 gold and purple beads. She used 46 gold beads and 30% of the purple beads. After that, the ratio of the number of gold beads to purple beads Marion had was 3 : 7.

1. What fraction of her purple beads did Marion use? Give your answer in the simplest form.
2. How many beads did Marion have in the end?

	Gold beads	Purple beads	Total
Before	3 u + 46	10 u	13 u + 46
Change	- 46	- 3 u
After	3 u	7 u	10 u
Comparing gold beads and purple beads in the end	3	7	10

(a)
30% = ³⁰₁₀₀ = ³₁₀

Fraction of her purple beads that Marion used = ³₁₀

(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 gold beads at first = 3 u + 46

Total number of beads at first
= 10 u + 3 u + 46
= 13 u + 46

13 u + 46 = 163
13 u = 163 - 46
13 u = 117

1 u = 117 ÷ 13 = 9

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

Total number of beads in the end
= 3 u + 7 u
= 10 u
= 10 x 9
= 90

Answer(s): (a)³₁₀; (b) 90