PSLE
Nora and Carl bought paintings at the prices shown below.

3 Large paintings for $8
5 Small paintings for $4

1. Nora bought an equal number of large and small paintings. She spent $112 more on the large ones. How many paintings did she buy altogether?
2. Carl 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 Nora 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 = $8
Cost of 15 large paintings = 5 x 8 = $40

Cost of 5 small paintings = $4
Cost of 15 small paintings = 3 x 4 = $12

Difference in the cost of buying 15 small paintings and 15 large paintings
= 40 - 12
= $28

Number of sets of paintings
= 112 ÷ 28
= 4

Number of paintings that Nora bought
= 4 x 2 x 15
= 120

(b)
Carl 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 8 and 4 is 8.

Number of large paintings that Carl bought
= 3 x (8 ÷ 8)
= 3 x 1
= 3

Number of the small paintings that Carl bought
= 5 x (8 ÷ 4)
= 5 x 2
= 10

Fraction of the paintings that Carl bought that were large
= ³_{3 + 10}
= ³₁₃

Answer(s): (a) 120; (b) ³₁₃