PSLE
Olivia and Jack bought jigsaw puzzles at the prices shown below.

2 Large jigsaw puzzles for $14
3 Small jigsaw puzzles for $10

1. Olivia bought an equal number of large and small jigsaw puzzles. She spent $88 more on the large ones. How many jigsaw puzzles did she buy altogether?
2. Jack spent an equal amount of money on the large and small jigsaw puzzles. What fraction of the jigsaw puzzles he bought were small?

(a)
Number of large and small jigsaw puzzles that Olivia bought is the same. Make the number of large and small jigsaw puzzles the same. LCM of 2 and 3 is 6.

Cost of 2 large jigsaw puzzles = $14
Cost of 6 large jigsaw puzzles = 3 x 14 = $42

Cost of 3 small jigsaw puzzles = $10
Cost of 6 small jigsaw puzzles = 2 x 10 = $20

Difference in the cost of buying 6 small jigsaw puzzles and 6 large jigsaw puzzles
= 42 - 20
= $22

Number of sets of jigsaw puzzles
= 88 ÷ 22
= 4

Number of jigsaw puzzles that Olivia bought
= 4 x 2 x 6
= 48

(b)
Jack 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 14 and 10 is 70.

Number of large jigsaw puzzles that Jack bought
= 2 x (70 ÷ 14)
= 2 x 5
= 10

Number of the small jigsaw puzzles that Jack bought
= 3 x (70 ÷ 10)
= 3 x 7
= 21

Fraction of the jigsaw puzzles that Jack bought that were small
= ²¹_{10 + 21}
= ²¹₃₁

Answer(s): (a) 48; (b) ²¹₃₁