PSLE
Hazel and Oliver bought paintings at the prices shown below.

4 Large paintings for $10
5 Small paintings for $6

1. Hazel bought an equal number of large and small paintings. She spent $78 more on the large ones. How many paintings did she buy altogether?
2. Oliver 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 Hazel bought is the same. Make the number of large and small paintings the same. LCM of 4 and 5 is 20.

Cost of 4 large paintings = $10
Cost of 20 large paintings = 5 x 10 = $50

Cost of 5 small paintings = $6
Cost of 20 small paintings = 4 x 6 = $24

Difference in the cost of buying 20 small paintings and 20 large paintings
= 50 - 24
= $26

Number of sets of paintings
= 78 ÷ 26
= 3

Number of paintings that Hazel bought
= 3 x 2 x 20
= 120

(b)
Oliver 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 10 and 6 is 30.

Number of large paintings that Oliver bought
= 4 x (30 ÷ 10)
= 4 x 3
= 12

Number of the small paintings that Oliver bought
= 5 x (30 ÷ 6)
= 5 x 5
= 25

Fraction of the paintings that Oliver bought that were large
= ¹²_{12 + 25}
= ¹²₃₇

Answer(s): (a) 120; (b) ¹²₃₇