PSLE
Joelle and Asher bought paintings at the prices shown below.

2 Large paintings for $12
3 Small paintings for $8

1. Joelle bought an equal number of large and small paintings. She spent $60 more on the large ones. How many paintings did she buy altogether?
2. Asher 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 Joelle 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 = $12
Cost of 6 large paintings = 3 x 12 = $36

Cost of 3 small paintings = $8
Cost of 6 small paintings = 2 x 8 = $16

Difference in the cost of buying 6 small paintings and 6 large paintings
= 36 - 16
= $20

Number of sets of paintings
= 60 ÷ 20
= 3

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

(b)
Asher 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 12 and 8 is 24.

Number of large paintings that Asher bought
= 2 x (24 ÷ 12)
= 2 x 2
= 4

Number of the small paintings that Asher bought
= 3 x (24 ÷ 8)
= 3 x 3
= 9

Fraction of the paintings that Asher bought that were large
= ⁴_{4 + 9}
= ⁴₁₃

Answer(s): (a) 36; (b) ⁴₁₃