PSLE
Cindy and Charlie bought paintings at the prices shown below.

4 Large paintings for $15
7 Small paintings for $9

1. Cindy bought an equal number of large and small paintings. She spent $207 more on the large ones. How many paintings did she buy altogether?
2. Charlie 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 Cindy 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 = $9
Cost of 28 small paintings = 4 x 9 = $36

Difference in the cost of buying 28 small paintings and 28 large paintings
= 105 - 36
= $69

Number of sets of paintings
= 207 ÷ 69
= 3

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

(b)
Charlie 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 9 is 45.

Number of large paintings that Charlie bought
= 4 x (45 ÷ 15)
= 4 x 3
= 12

Number of the small paintings that Charlie bought
= 7 x (45 ÷ 9)
= 7 x 5
= 35

Fraction of the paintings that Charlie bought that were small
= ³⁵_{12 + 35}
= ³⁵₄₇

Answer(s): (a) 168; (b) ³⁵₄₇