PSLE
Cathy and Brandon bought paintings at the prices shown below.

2 Large paintings for $12
5 Small paintings for $8

1. Cathy bought an equal number of large and small paintings. She spent $176 more on the large ones. How many paintings did she buy altogether?
2. Brandon 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 Cathy 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 = $12
Cost of 10 large paintings = 5 x 12 = $60

Cost of 5 small paintings = $8
Cost of 10 small paintings = 2 x 8 = $16

Difference in the cost of buying 10 small paintings and 10 large paintings
= 60 - 16
= $44

Number of sets of paintings
= 176 ÷ 44
= 4

Number of paintings that Cathy bought
= 4 x 2 x 10
= 80

(b)
Brandon 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 12 and 8 is 24.

Number of large paintings that Brandon bought
= 2 x (24 ÷ 12)
= 2 x 2
= 4

Number of the small paintings that Brandon bought
= 5 x (24 ÷ 8)
= 5 x 3
= 15

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

Answer(s): (a) 80; (b) ⁴₁₉