PSLE
Gem and Vaidev bought storybooks at the prices shown below.

3 Large storybooks for $8
4 Small storybooks for $6

1. Gem bought an equal number of large and small storybooks. She spent $56 more on the large ones. How many storybooks did she buy altogether?
2. Vaidev 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 Gem bought is the same. Make the number of large and small storybooks the same. LCM of 3 and 4 is 12.

Cost of 3 large storybooks = $8
Cost of 12 large storybooks = 4 x 8 = $32

Cost of 4 small storybooks = $6
Cost of 12 small storybooks = 3 x 6 = $18

Difference in the cost of buying 12 small storybooks and 12 large storybooks
= 32 - 18
= $14

Number of sets of storybooks
= 56 ÷ 14
= 4

Number of storybooks that Gem bought
= 4 x 2 x 12
= 96

(b)
Vaidev 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 8 and 6 is 24.

Number of large storybooks that Vaidev bought
= 3 x (24 ÷ 8)
= 3 x 3
= 9

Number of the small storybooks that Vaidev bought
= 4 x (24 ÷ 6)
= 4 x 4
= 16

Fraction of the storybooks that Vaidev bought that were small
= ¹⁶_{9 + 16}
= ¹⁶₂₅

Answer(s): (a) 96; (b) ¹⁶₂₅