PSLE
Hazel and Japheth bought storybooks at the prices shown below.

2 Large storybooks for $6
3 Small storybooks for $4

1. Hazel bought an equal number of large and small storybooks. She spent $20 more on the large ones. How many storybooks did she buy altogether?
2. Japheth spent an equal amount of money on the large and small storybooks. What fraction of the storybooks he bought were large?

(a)
Number of large and small storybooks that Hazel bought is the same. Make the number of large and small storybooks the same. LCM of 2 and 3 is 6.

Cost of 2 large storybooks = $6
Cost of 6 large storybooks = 3 x 6 = $18

Cost of 3 small storybooks = $4
Cost of 6 small storybooks = 2 x 4 = $8

Difference in the cost of buying 6 small storybooks and 6 large storybooks
= 18 - 8
= $10

Number of sets of storybooks
= 20 ÷ 10
= 2

Number of storybooks that Hazel bought
= 2 x 2 x 6
= 24

(b)
Japheth 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 6 and 4 is 12.

Number of large storybooks that Japheth bought
= 2 x (12 ÷ 6)
= 2 x 2
= 4

Number of the small storybooks that Japheth bought
= 3 x (12 ÷ 4)
= 3 x 3
= 9

Fraction of the storybooks that Japheth bought that were large
= ⁴_{4 + 9}
= ⁴₁₃

Answer(s): (a) 24; (b) ⁴₁₃