PSLE
Linda had a total of 91 purple and gold beads. She used 26 purple beads and 40% of the gold beads. After that, the ratio of the number of purple beads to gold beads Linda had was 8 : 3.

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

	Purple	Gold	Total
Before	8 u + 26	5 u	13 u + 26
Change	- 26	- 2 u
After	8 u	3 u	11 u
Comparing purple beads and gold beads in the end	8	3	11

(a)
40% = ⁴⁰₁₀₀ = ²₅

Fraction of her gold beads that Linda used = ²₅

Fraction of her gold beads that Linda was left with
= 1 - ²₅
= ³₅

(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 purple beads at first = 8 u + 26

Total number of beads at first
= 5 u + 8 u + 26
= 13 u + 26

13 u + 26 = 91
13 u = 91 - 26
13 u = 65

1 u = 65 ÷ 13 = 5

Number of gold beads in the end = 3 u
Number of purple beads in the end = 8 u

Number of more purple beads than gold beads that Linda had in the end
= 8 u - 3 u
= 5 u
= 5 x 5
= 25

Answer(s): (a)³₅; (b) 25