PSLE
Dana had a total of 309 silver and yellow beads. She used 21 silver beads and 90% of the yellow beads. After that, the ratio of the number of silver beads to yellow beads Dana had was 6 : 1.

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

	Silver	Yellow	Total
Before	6 u + 21	10 u	16 u + 21
Change	- 21	- 9 u
After	6 u	1 u	7 u
Comparing silver beads and yellow beads in the end	6	1	7

(a)
90% = ⁹⁰₁₀₀ = ⁹₁₀

Fraction of her yellow beads that Dana used = ⁹₁₀

Fraction of her yellow beads that Dana was left with
= 1 - ⁹₁₀
= ¹₁₀

(b)
The number of yellow 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 yellow beads at first = 10 u
Number of silver beads at first = 6 u + 21

Total number of beads at first
= 10 u + 6 u + 21
= 16 u + 21

16 u + 21 = 309
16 u = 309 - 21
16 u = 288

1 u = 288 ÷ 16 = 18

Number of yellow beads in the end = 1 u
Number of silver beads in the end = 6 u

Number of more silver beads than yellow beads that Dana had in the end
= 6 u - 1 u
= 5 u
= 5 x 18
= 90

Answer(s): (a)¹₁₀; (b) 90