PSLE
Esther had a total of 208 blue and silver beads. She used 10 blue beads and 25% of the silver beads. After that, the ratio of the number of blue beads to silver beads Esther had was 7 : 3.

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

	Blue	Silver	Total
Before	7 u + 10	4 u	11 u + 10
Change	- 10	- 1 u
After	7 u	3 u	10 u
Comparing blue beads and silver beads in the end	7	3	10

(a)
25% = ²⁵₁₀₀ = ¹₄

Fraction of her silver beads that Esther used = ¹₄

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

(b)
The number of silver 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 silver beads at first = 4 u
Number of blue beads at first = 7 u + 10

Total number of beads at first
= 4 u + 7 u + 10
= 11 u + 10

11 u + 10 = 208
11 u = 208 - 10
11 u = 198

1 u = 198 ÷ 11 = 18

Number of silver beads in the end = 3 u
Number of blue beads in the end = 7 u

Number of more blue beads than silver beads that Esther had in the end
= 7 u - 3 u
= 4 u
= 4 x 18
= 72

Answer(s): (a)³₄; (b) 72