PSLE
Zoe had a total of 113 red and gold beads. She used 41 red beads and 60% of the gold beads. After that, the ratio of the number of red beads to gold beads Zoe had was 7 : 2.

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

	Red	Gold	Total
Before	7 u + 41	5 u	12 u + 41
Change	- 41	- 3 u
After	7 u	2 u	9 u
Comparing red beads and gold beads in the end	7	2	9

(a)
60% = ⁶⁰₁₀₀ = ³₅

Fraction of her gold beads that Zoe used = ³₅

Fraction of her gold beads that Zoe was left with
= 1 - ³₅
= ²₅

(b)
The number of gold 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 gold beads at first = 5 u
Number of red beads at first = 7 u + 41

Total number of beads at first
= 5 u + 7 u + 41
= 12 u + 41

12 u + 41 = 113
12 u = 113 - 41
12 u = 72

1 u = 72 ÷ 12 = 6

Number of gold beads in the end = 2 u
Number of red beads in the end = 7 u

Number of more red beads than gold beads that Zoe had in the end
= 7 u - 2 u
= 5 u
= 5 x 6
= 30

Answer(s): (a)²₅; (b) 30