PSLE
Esther had a total of 136 purple and red beads. She used 45 purple beads and 75% of the red beads. After that, the ratio of the number of purple beads to red beads Esther had was 9 : 1.

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

	Purple	Red	Total
Before	9 u + 45	4 u	13 u + 45
Change	- 45	- 3 u
After	9 u	1 u	10 u
Comparing purple beads and red beads in the end	9	1	10

(a)
75% = ⁷⁵₁₀₀ = ³₄

Fraction of her red beads that Esther used = ³₄

Fraction of her red beads that Esther was left with
= 1 - ³₄
= ¹₄

(b)
The number of red 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 red beads at first = 4 u
Number of purple beads at first = 9 u + 45

Total number of beads at first
= 4 u + 9 u + 45
= 13 u + 45

13 u + 45 = 136
13 u = 136 - 45
13 u = 91

1 u = 91 ÷ 13 = 7

Number of red beads in the end = 1 u
Number of purple beads in the end = 9 u

Number of more purple beads than red beads that Esther had in the end
= 9 u - 1 u
= 8 u
= 8 x 7
= 56

Answer(s): (a)¹₄; (b) 56