PSLE
Gwen had a total of 119 red and yellow beads. She used 41 red beads and 90% of the yellow beads. After that, the ratio of the number of red beads to yellow beads Gwen had was 3 : 1.

1. What fraction of her yellow beads did Gwen use? Give your answer in the simplest form.
2. How many beads did Gwen have in the end?

	Red beads	Yellow beads	Total
Before	3 u + 41	10 u	13 u + 41
Change	- 41	- 9 u
After	3 u	1 u	4 u
Comparing red beads and yellow beads in the end	3	1	4

(a)
90% = ⁹⁰₁₀₀ = ⁹₁₀

Fraction of her yellow beads that Gwen used = ⁹₁₀

(b)
The number of yellow 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 yellow beads at first = 10 u
Number of red beads at first = 3 u + 41

Total number of beads at first
= 10 u + 3 u + 41
= 13 u + 41

13 u + 41 = 119
13 u = 119 - 41
13 u = 78

1 u = 78 ÷ 13 = 6

Number of yellow beads in the end = 1 u
Number of red beads in the end = 3 u

Total number of beads in the end
= 3 u + 1 u
= 4 u
= 4 x 6
= 24

Answer(s): (a)⁹₁₀; (b) 24