PSLE
Jen and Cody bought paintings at the prices shown below.

2 Large paintings for $15
3 Small paintings for $12

1. Jen bought an equal number of large and small paintings. She spent $63 more on the large ones. How many paintings did she buy altogether?
2. Cody spent an equal amount of money on the large and small paintings. What fraction of the paintings he bought were large?

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

Cost of 2 large paintings = $15
Cost of 6 large paintings = 3 x 15 = $45

Cost of 3 small paintings = $12
Cost of 6 small paintings = 2 x 12 = $24

Difference in the cost of buying 6 small paintings and 6 large paintings
= 45 - 24
= $21

Number of sets of paintings
= 63 ÷ 21
= 3

Number of paintings that Jen bought
= 3 x 2 x 6
= 36

(b)
Cody spent an equal amount of money on the large and small paintings.  Make the amount of money spent on the large and small paintings the same.
LCM of 15 and 12 is 60.

Number of large paintings that Cody bought
= 2 x (60 ÷ 15)
= 2 x 4
= 8

Number of the small paintings that Cody bought
= 3 x (60 ÷ 12)
= 3 x 5
= 15

Fraction of the paintings that Cody bought that were large
= ⁸_{8 + 15}
= ⁸₂₃

Answer(s): (a) 36; (b) ⁸₂₃