PSLE
Hilda and Luis bought jigsaw puzzles at the prices shown below.

2 Large jigsaw puzzles for $9
3 Small jigsaw puzzles for $5

1. Hilda bought an equal number of large and small jigsaw puzzles. She spent $51 more on the large ones. How many jigsaw puzzles did she buy altogether?
2. Luis 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 Hilda 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 = $9
Cost of 6 large jigsaw puzzles = 3 x 9 = $27

Cost of 3 small jigsaw puzzles = $5
Cost of 6 small jigsaw puzzles = 2 x 5 = $10

Difference in the cost of buying 6 small jigsaw puzzles and 6 large jigsaw puzzles
= 27 - 10
= $17

Number of sets of jigsaw puzzles
= 51 ÷ 17
= 3

Number of jigsaw puzzles that Hilda bought
= 3 x 2 x 6
= 36

(b)
Luis 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 9 and 5 is 45.

Number of large jigsaw puzzles that Luis bought
= 2 x (45 ÷ 9)
= 2 x 5
= 10

Number of the small jigsaw puzzles that Luis bought
= 3 x (45 ÷ 5)
= 3 x 9
= 27

Fraction of the jigsaw puzzles that Luis bought that were small
= ²⁷_{10 + 27}
= ²⁷₃₇

Answer(s): (a) 36; (b) ²⁷₃₇