PSLE
Kathy had a total of 143 purple and black beads. She used 33 purple beads and 75% of the black beads. After that, the ratio of the number of purple beads to black beads Kathy had was 6 : 1.

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

	Purple beads	Black beads	Total
Before	6 u + 33	4 u	10 u + 33
Change	- 33	- 3 u
After	6 u	1 u	7 u
Comparing purple beads and black beads in the end	6	1	7

(a)
75% = ⁷⁵₁₀₀ = ³₄

Fraction of her black beads that Kathy used = ³₄

(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 = 6 u + 33

Total number of beads at first
= 4 u + 6 u + 33
= 10 u + 33

10 u + 33 = 143
10 u = 143 - 33
10 u = 110

1 u = 110 ÷ 10 = 11

Number of black beads in the end = 1 u
Number of purple beads in the end = 6 u

Total number of beads in the end
= 6 u + 1 u
= 7 u
= 7 x 11
= 77

Answer(s): (a)³₄; (b) 77