PSLE
Victoria had a total of 187 red and black beads. She used 11 red beads and 75% of the black beads. After that, the ratio of the number of red beads to black beads Victoria had was 7 : 1.

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

	Red	Black	Total
Before	7 u + 11	4 u	11 u + 11
Change	- 11	- 3 u
After	7 u	1 u	8 u
Comparing red beads and black beads in the end	7	1	8

(a)
75% = ⁷⁵₁₀₀ = ³₄

Fraction of her black beads that Victoria used = ³₄

Fraction of her black beads that Victoria was left with
= 1 - ³₄
= ¹₄

(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 = 4 u
Number of red beads at first = 7 u + 11

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

11 u + 11 = 187
11 u = 187 - 11
11 u = 176

1 u = 176 ÷ 11 = 16

Number of black beads in the end = 1 u
Number of red beads in the end = 7 u

Number of more red beads than black beads that Victoria had in the end
= 7 u - 1 u
= 6 u
= 6 x 16
= 96

Answer(s): (a)¹₄; (b) 96