PSLE
Gabby had a total of 159 pink and orange beads. She used 31 pink beads and 50% of the orange beads. After that, the ratio of the number of pink beads to orange beads Gabby had was 6 : 1.

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

	Pink	Orange	Total
Before	6 u + 31	2 u	8 u + 31
Change	- 31	- 1 u
After	6 u	1 u	7 u
Comparing pink beads and orange beads in the end	6	1	7

(a)
50% = ⁵⁰₁₀₀ = ¹₂

Fraction of her orange beads that Gabby used = ¹₂

Fraction of her orange beads that Gabby was left with
= 1 - ¹₂
= ¹₂

(b)
The number of orange 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 orange beads at first = 2 u
Number of pink beads at first = 6 u + 31

Total number of beads at first
= 2 u + 6 u + 31
= 8 u + 31

8 u + 31 = 159
8 u = 159 - 31
8 u = 128

1 u = 128 ÷ 8 = 16

Number of orange beads in the end = 1 u
Number of pink beads in the end = 6 u

Number of more pink beads than orange beads that Gabby had in the end
= 6 u - 1 u
= 5 u
= 5 x 16
= 80

Answer(s): (a)¹₂; (b) 80