PSLE
Linda and Xavier bought jigsaw puzzles at the prices shown below.

3 Large jigsaw puzzles for $8
5 Small jigsaw puzzles for $6

1. Linda bought an equal number of large and small jigsaw puzzles. She spent $44 more on the large ones. How many jigsaw puzzles did she buy altogether?
2. Xavier 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 Linda bought is the same. Make the number of large and small jigsaw puzzles the same. LCM of 3 and 5 is 15.

Cost of 3 large jigsaw puzzles = $8
Cost of 15 large jigsaw puzzles = 5 x 8 = $40

Cost of 5 small jigsaw puzzles = $6
Cost of 15 small jigsaw puzzles = 3 x 6 = $18

Difference in the cost of buying 15 small jigsaw puzzles and 15 large jigsaw puzzles
= 40 - 18
= $22

Number of sets of jigsaw puzzles
= 44 ÷ 22
= 2

Number of jigsaw puzzles that Linda bought
= 2 x 2 x 15
= 60

(b)
Xavier 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 8 and 6 is 24.

Number of large jigsaw puzzles that Xavier bought
= 3 x (24 ÷ 8)
= 3 x 3
= 9

Number of the small jigsaw puzzles that Xavier bought
= 5 x (24 ÷ 6)
= 5 x 4
= 20

Fraction of the jigsaw puzzles that Xavier bought that were small
= ²⁰_{9 + 20}
= ²⁰₂₉

Answer(s): (a) 60; (b) ²⁰₂₉