PSLE
Abi and Pierre bought paintings at the prices shown below.

2 Large paintings for $9
5 Small paintings for $6

1. Abi bought an equal number of large and small paintings. She spent $99 more on the large ones. How many paintings did she buy altogether?
2. Pierre 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 Abi bought is the same. Make the number of large and small paintings the same. LCM of 2 and 5 is 10.

Cost of 2 large paintings = $9
Cost of 10 large paintings = 5 x 9 = $45

Cost of 5 small paintings = $6
Cost of 10 small paintings = 2 x 6 = $12

Difference in the cost of buying 10 small paintings and 10 large paintings
= 45 - 12
= $33

Number of sets of paintings
= 99 ÷ 33
= 3

Number of paintings that Abi bought
= 3 x 2 x 10
= 60

(b)
Pierre 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 Pierre bought
= 2 x (18 ÷ 9)
= 2 x 2
= 4

Number of the small paintings that Pierre bought
= 5 x (18 ÷ 6)
= 5 x 3
= 15

Fraction of the paintings that Pierre bought that were large
= ⁴_{4 + 15}
= ⁴₁₉

Answer(s): (a) 60; (b) ⁴₁₉