PSLE
Gem and Rael bought paintings at the prices shown below.

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

1. Gem 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. Rael 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 Gem bought is the same. Make the number of large and small paintings the same. LCM of 3 and 5 is 15.

Cost of 3 large paintings = $15
Cost of 15 large paintings = 5 x 15 = $75

Cost of 5 small paintings = $12
Cost of 15 small paintings = 3 x 12 = $36

Difference in the cost of buying 15 small paintings and 15 large paintings
= 75 - 36
= $39

Number of sets of paintings
= 78 ÷ 39
= 2

Number of paintings that Gem bought
= 2 x 2 x 15
= 60

(b)
Rael 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 Rael bought
= 3 x (60 ÷ 15)
= 3 x 4
= 12

Number of the small paintings that Rael bought
= 5 x (60 ÷ 12)
= 5 x 5
= 25

Fraction of the paintings that Rael bought that were small
= ²⁵_{12 + 25}
= ²⁵₃₇

Answer(s): (a) 60; (b) ²⁵₃₇