PSLE
Kylie and Reggie bought paintings at the prices shown below.

4 Large paintings for $9
7 Small paintings for $6

1. Kylie bought an equal number of large and small paintings. She spent $156 more on the large ones. How many paintings did she buy altogether?
2. Reggie 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 Kylie 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 = $9
Cost of 28 large paintings = 7 x 9 = $63

Cost of 7 small paintings = $6
Cost of 28 small paintings = 4 x 6 = $24

Difference in the cost of buying 28 small paintings and 28 large paintings
= 63 - 24
= $39

Number of sets of paintings
= 156 ÷ 39
= 4

Number of paintings that Kylie bought
= 4 x 2 x 28
= 224

(b)
Reggie 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 9 and 6 is 18.

Number of large paintings that Reggie bought
= 4 x (18 ÷ 9)
= 4 x 2
= 8

Number of the small paintings that Reggie bought
= 7 x (18 ÷ 6)
= 7 x 3
= 21

Fraction of the paintings that Reggie bought that were large
= ⁸_{8 + 21}
= ⁸₂₉

Answer(s): (a) 224; (b) ⁸₂₉