PSLE
Eva and Henry bought paintings at the prices shown below.

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

1. Eva bought an equal number of large and small paintings. She spent $40 more on the large ones. How many paintings did she buy altogether?
2. Henry 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 Eva bought is the same. Make the number of large and small paintings the same. LCM of 3 and 4 is 12.

Cost of 3 large paintings = $8
Cost of 12 large paintings = 4 x 8 = $32

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

Difference in the cost of buying 12 small paintings and 12 large paintings
= 32 - 12
= $20

Number of sets of paintings
= 40 ÷ 20
= 2

Number of paintings that Eva bought
= 2 x 2 x 12
= 48

(b)
Henry 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 Henry bought
= 3 x (8 ÷ 8)
= 3 x 1
= 3

Number of the small paintings that Henry bought
= 4 x (8 ÷ 4)
= 4 x 2
= 8

Fraction of the paintings that Henry bought that were large
= ³_{3 + 8}
= ³₁₁

Answer(s): (a) 48; (b) ³₁₁