PSLE
Penelope and Ethan bought paintings at the prices shown below.

4 Large paintings for $15
7 Small paintings for $10

1. Penelope bought an equal number of large and small paintings. She spent $195 more on the large ones. How many paintings did she buy altogether?
2. Ethan spent an equal amount of money on the large and small paintings. What fraction of the paintings he bought were small?

(a)
Number of large and small paintings that Penelope bought is the same. Make the number of large and small paintings the same. LCM of 4 and 7 is 28.

Cost of 4 large paintings = $15
Cost of 28 large paintings = 7 x 15 = $105

Cost of 7 small paintings = $10
Cost of 28 small paintings = 4 x 10 = $40

Difference in the cost of buying 28 small paintings and 28 large paintings
= 105 - 40
= $65

Number of sets of paintings
= 195 ÷ 65
= 3

Number of paintings that Penelope bought
= 3 x 2 x 28
= 168

(b)
Ethan 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 10 is 30.

Number of large paintings that Ethan bought
= 4 x (30 ÷ 15)
= 4 x 2
= 8

Number of the small paintings that Ethan bought
= 7 x (30 ÷ 10)
= 7 x 3
= 21

Fraction of the paintings that Ethan bought that were small
= ²¹_{8 + 21}
= ²¹₂₉

Answer(s): (a) 168; (b) ²¹₂₉