PSLE
Nicole and Justin bought jigsaw puzzles at the prices shown below.

4 Large jigsaw puzzles for $10
7 Small jigsaw puzzles for $4

1. Nicole bought an equal number of large and small jigsaw puzzles. She spent $162 more on the large ones. How many jigsaw puzzles did she buy altogether?
2. Justin 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 Nicole bought is the same. Make the number of large and small jigsaw puzzles the same. LCM of 4 and 7 is 28.

Cost of 4 large jigsaw puzzles = $10
Cost of 28 large jigsaw puzzles = 7 x 10 = $70

Cost of 7 small jigsaw puzzles = $4
Cost of 28 small jigsaw puzzles = 4 x 4 = $16

Difference in the cost of buying 28 small jigsaw puzzles and 28 large jigsaw puzzles
= 70 - 16
= $54

Number of sets of jigsaw puzzles
= 162 ÷ 54
= 3

Number of jigsaw puzzles that Nicole bought
= 3 x 2 x 28
= 168

(b)
Justin 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 10 and 4 is 20.

Number of large jigsaw puzzles that Justin bought
= 4 x (20 ÷ 10)
= 4 x 2
= 8

Number of the small jigsaw puzzles that Justin bought
= 7 x (20 ÷ 4)
= 7 x 5
= 35

Fraction of the jigsaw puzzles that Justin bought that were small
= ³⁵_{8 + 35}
= ³⁵₄₃

Answer(s): (a) 168; (b) ³⁵₄₃