PSLE
Cathy and Cole bought storybooks at the prices shown below.

4 Large storybooks for $10
7 Small storybooks for $6

1. Cathy bought an equal number of large and small storybooks. She spent $138 more on the large ones. How many storybooks did she buy altogether?
2. Cole 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 Cathy 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 = $10
Cost of 28 large storybooks = 7 x 10 = $70

Cost of 7 small storybooks = $6
Cost of 28 small storybooks = 4 x 6 = $24

Difference in the cost of buying 28 small storybooks and 28 large storybooks
= 70 - 24
= $46

Number of sets of storybooks
= 138 ÷ 46
= 3

Number of storybooks that Cathy bought
= 3 x 2 x 28
= 168

(b)
Cole 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 10 and 6 is 30.

Number of large storybooks that Cole bought
= 4 x (30 ÷ 10)
= 4 x 3
= 12

Number of the small storybooks that Cole bought
= 7 x (30 ÷ 6)
= 7 x 5
= 35

Fraction of the storybooks that Cole bought that were small
= ³⁵_{12 + 35}
= ³⁵₄₇

Answer(s): (a) 168; (b) ³⁵₄₇