PSLE
Jane had a total of 156 yellow and black beads. She used 13 yellow beads and 90% of the black beads. After that, the ratio of the number of yellow beads to black beads Jane had was 3 : 1.

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

	Yellow	Black	Total
Before	3 u + 13	10 u	13 u + 13
Change	- 13	- 9 u
After	3 u	1 u	4 u
Comparing yellow beads and black beads in the end	3	1	4

(a)
90% = ⁹⁰₁₀₀ = ⁹₁₀

Fraction of her black beads that Jane used = ⁹₁₀

Fraction of her black beads that Jane was left with
= 1 - ⁹₁₀
= ¹₁₀

(b)
The number of black 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 black beads at first = 10 u
Number of yellow beads at first = 3 u + 13

Total number of beads at first
= 10 u + 3 u + 13
= 13 u + 13

13 u + 13 = 156
13 u = 156 - 13
13 u = 143

1 u = 143 ÷ 13 = 11

Number of black beads in the end = 1 u
Number of yellow beads in the end = 3 u

Number of more yellow beads than black beads that Jane had in the end
= 3 u - 1 u
= 2 u
= 2 x 11
= 22

Answer(s): (a)¹₁₀; (b) 22