PSLE
Jane had a total of 190 pink and gold beads. She used 21 pink beads and 80% of the gold beads. After that, the ratio of the number of pink beads to gold beads Jane had was 8 : 1.

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

	Pink	Gold	Total
Before	8 u + 21	5 u	13 u + 21
Change	- 21	- 4 u
After	8 u	1 u	9 u
Comparing pink beads and gold beads in the end	8	1	9

(a)
80% = ⁸⁰₁₀₀ = ⁴₅

Fraction of her gold beads that Jane used = ⁴₅

Fraction of her gold beads that Jane was left with
= 1 - ⁴₅
= ¹₅

(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 = 5 u
Number of pink beads at first = 8 u + 21

Total number of beads at first
= 5 u + 8 u + 21
= 13 u + 21

13 u + 21 = 190
13 u = 190 - 21
13 u = 169

1 u = 169 ÷ 13 = 13

Number of gold beads in the end = 1 u
Number of pink beads in the end = 8 u

Number of more pink beads than gold beads that Jane had in the end
= 8 u - 1 u
= 7 u
= 7 x 13
= 91

Answer(s): (a)¹₅; (b) 91