PSLE
Olivia and Wesley bought storybooks at the prices shown below.

4 Large storybooks for $15
7 Small storybooks for $10

1. Olivia bought an equal number of large and small storybooks. She spent $260 more on the large ones. How many storybooks did she buy altogether?
2. Wesley spent an equal amount of money on the large and small storybooks. What fraction of the storybooks he bought were small?

(a)
Number of large and small storybooks that Olivia bought is the same. Make the number of large and small storybooks the same. LCM of 4 and 7 is 28.

Cost of 4 large storybooks = $15
Cost of 28 large storybooks = 7 x 15 = $105

Cost of 7 small storybooks = $10
Cost of 28 small storybooks = 4 x 10 = $40

Difference in the cost of buying 28 small storybooks and 28 large storybooks
= 105 - 40
= $65

Number of sets of storybooks
= 260 ÷ 65
= 4

Number of storybooks that Olivia bought
= 4 x 2 x 28
= 224

(b)
Wesley spent an equal amount of money on the large and small storybooks. Make the amount of money spent on the large and small storybooks the same.
LCM of 15 and 10 is 30.

Number of large storybooks that Wesley bought
= 4 x (30 ÷ 15)
= 4 x 2
= 8

Number of the small storybooks that Wesley bought
= 7 x (30 ÷ 10)
= 7 x 3
= 21

Fraction of the storybooks that Wesley bought that were small
= ²¹_{8 + 21}
= ²¹₂₉

Answer(s): (a) 224; (b) ²¹₂₉