PSLE
Elyse had a total of 143 purple and gold beads. She used 33 purple beads and 30% of the gold beads. After that, the ratio of the number of purple beads to gold beads Elyse had was 1 : 7.

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

	Purple beads	Gold beads	Total
Before	1 u + 33	10 u	11 u + 33
Change	- 33	- 3 u
After	1 u	7 u	8 u
Comparing purple beads and gold beads in the end	1	7	8

(a)
30% = ³⁰₁₀₀ = ³₁₀

Fraction of her gold beads that Elyse used = ³₁₀

(b)
The number of gold 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 gold beads at first = 10 u
Number of purple beads at first = 1 u + 33

Total number of beads at first
= 10 u + 1 u + 33
= 11 u + 33

11 u + 33 = 143
11 u = 143 - 33
11 u = 110

1 u = 110 ÷ 11 = 10

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

Total number of beads in the end
= 1 u + 7 u
= 8 u
= 8 x 10
= 80

Answer(s): (a)³₁₀; (b) 80