PSLE
Gem and Michael bought jigsaw puzzles at the prices shown below.

4 Large jigsaw puzzles for $6
5 Small jigsaw puzzles for $4

1. Gem bought an equal number of large and small jigsaw puzzles. She spent $42 more on the large ones. How many jigsaw puzzles did she buy altogether?
2. Michael spent an equal amount of money on the large and small jigsaw puzzles. What fraction of the jigsaw puzzles he bought were large?

(a)
Number of large and small jigsaw puzzles that Gem bought is the same. Make the number of large and small jigsaw puzzles the same. LCM of 4 and 5 is 20.

Cost of 4 large jigsaw puzzles = $6
Cost of 20 large jigsaw puzzles = 5 x 6 = $30

Cost of 5 small jigsaw puzzles = $4
Cost of 20 small jigsaw puzzles = 4 x 4 = $16

Difference in the cost of buying 20 small jigsaw puzzles and 20 large jigsaw puzzles
= 30 - 16
= $14

Number of sets of jigsaw puzzles
= 42 ÷ 14
= 3

Number of jigsaw puzzles that Gem bought
= 3 x 2 x 20
= 120

(b)
Michael spent an equal amount of money on the large and small jigsaw puzzles.  Make the amount of money spent on the large and small jigsaw puzzles the same.
LCM of 6 and 4 is 12.

Number of large jigsaw puzzles that Michael bought
= 4 x (12 ÷ 6)
= 4 x 2
= 8

Number of the small jigsaw puzzles that Michael bought
= 5 x (12 ÷ 4)
= 5 x 3
= 15

Fraction of the jigsaw puzzles that Michael bought that were large
= ⁸_{8 + 15}
= ⁸₂₃

Answer(s): (a) 120; (b) ⁸₂₃