PSLE
Emma and Elijah bought paintings at the prices shown below.

4 Large paintings for $15
5 Small paintings for $9

1. Emma 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. Elijah 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 Emma bought is the same. Make the number of large and small paintings the same. LCM of 4 and 5 is 20.

Cost of 4 large paintings = $15
Cost of 20 large paintings = 5 x 15 = $75

Cost of 5 small paintings = $9
Cost of 20 small paintings = 4 x 9 = $36

Difference in the cost of buying 20 small paintings and 20 large paintings
= 75 - 36
= $39

Number of sets of paintings
= 156 ÷ 39
= 4

Number of paintings that Emma bought
= 4 x 2 x 20
= 160

(b)
Elijah 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 15 and 9 is 45.

Number of large paintings that Elijah bought
= 4 x (45 ÷ 15)
= 4 x 3
= 12

Number of the small paintings that Elijah bought
= 5 x (45 ÷ 9)
= 5 x 5
= 25

Fraction of the paintings that Elijah bought that were large
= ¹²_{12 + 25}
= ¹²₃₇

Answer(s): (a) 160; (b) ¹²₃₇