PSLE
Xuan and Dylan bought paintings at the prices shown below.

2 Large paintings for $10
5 Small paintings for $8

1. Xuan bought an equal number of large and small paintings. She spent $102 more on the large ones. How many paintings did she buy altogether?
2. Dylan spent an equal amount of money on the large and small paintings. What fraction of the paintings he bought were small?

(a)
Number of large and small paintings that Xuan 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 = $10
Cost of 10 large paintings = 5 x 10 = $50

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
= 50 - 16
= $34

Number of sets of paintings
= 102 ÷ 34
= 3

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

(b)
Dylan 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 10 and 8 is 40.

Number of large paintings that Dylan bought
= 2 x (40 ÷ 10)
= 2 x 4
= 8

Number of the small paintings that Dylan bought
= 5 x (40 ÷ 8)
= 5 x 5
= 25

Fraction of the paintings that Dylan bought that were small
= ²⁵_{8 + 25}
= ²⁵₃₃

Answer(s): (a) 60; (b) ²⁵₃₃