PSLE
A box contained gold and green beads. At first, the number of gold beads was ¹₄ the number of green beads. After ¹₃ of the gold beads and ⁵₉ of the green beads were used, 110 beads were left.

1. What fraction of the beads were used? Leave your answer in the simplest form.
2. How many beads were there in the box at first?

	Gold	Green
Comparing gold beads and green beads at first	1x9 = 9 u	4x9 = 36 u
Before	3x3 = 9 u	9x4 = 36 u
Change	- 1x3 =  - 3 u	- 5x4 = - 20 u
After	2x3 =  6 u	4x4 = 16 u

(a)
The number of green beads at first is repeated. Make the number of green beads at first the same. LCM of 4 and 9 is 36.

The number of gold beads at first is repeated.

Since the number of gold beads at first is 9 u, we make the total number of gold beads at first the same by multiplying 3 by 3 to become 9 u too.

Fraction of the beads used
= ^{3 + 20}_{9 + 36} 
= ²³₄₅

(b)
Number of beads left
= 6 u + 16 u
= 22 u

22 u = 110

1 u = 110 ÷ 22 = 5

Number of beads at first
= 45 u
= 45 x 5
= 225

Answer(s): (a) ²³₄₅; (b) 225