PSLE
Sabrina had a total of 261 black and purple beads. She used 23 black beads and 25% of the purple beads. After that, the ratio of the number of black beads to purple beads Sabrina had was 10 : 3.

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

	Black	Purple	Total
Before	10 u + 23	4 u	14 u + 23
Change	- 23	- 1 u
After	10 u	3 u	13 u
Comparing black beads and purple beads in the end	10	3	13

(a)
25% = ²⁵₁₀₀ = ¹₄

Fraction of her purple beads that Sabrina used = ¹₄

Fraction of her purple beads that Sabrina was left with
= 1 - ¹₄
= ³₄

(b)
The number of purple 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 purple beads at first = 4 u
Number of black beads at first = 10 u + 23

Total number of beads at first
= 4 u + 10 u + 23
= 14 u + 23

14 u + 23 = 261
14 u = 261 - 23
14 u = 238

1 u = 238 ÷ 14 = 17

Number of purple beads in the end = 3 u
Number of black beads in the end = 10 u

Number of more black beads than purple beads that Sabrina had in the end
= 10 u - 3 u
= 7 u
= 7 x 17
= 119

Answer(s): (a)³₄; (b) 119