PSLE
Gabby had a total of 155 purple and black beads. She used 23 purple beads and 75% of the black beads. After that, the ratio of the number of purple beads to black beads Gabby had was 7 : 1.

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

	Purple	Black	Total
Before	7 u + 23	4 u	11 u + 23
Change	- 23	- 3 u
After	7 u	1 u	8 u
Comparing purple beads and black beads in the end	7	1	8

(a)
75% = ⁷⁵₁₀₀ = ³₄

Fraction of her black beads that Gabby used = ³₄

Fraction of her black beads that Gabby 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 purple beads at first = 7 u + 23

Total number of beads at first
= 4 u + 7 u + 23
= 11 u + 23

11 u + 23 = 155
11 u = 155 - 23
11 u = 132

1 u = 132 ÷ 11 = 12

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

Number of more purple beads than black beads that Gabby had in the end
= 7 u - 1 u
= 6 u
= 6 x 12
= 72

Answer(s): (a)¹₄; (b) 72