PSLE
Dana and Japheth bought pillows at the prices shown below.

2 Large pillows for $10
3 Small pillows for $8

1. Dana bought an equal number of large and small pillows. She spent $42 more on the large ones. How many pillows did she buy altogether?
2. Japheth spent an equal amount of money on the large and small pillows. What fraction of the pillows he bought were small?

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

Cost of 2 large pillows = $10
Cost of 6 large pillows = 3 x 10 = $30

Cost of 3 small pillows = $8
Cost of 6 small pillows = 2 x 8 = $16

Difference in the cost of buying 6 small pillows and 6 large pillows
= 30 - 16
= $14

Number of sets of pillows
= 42 ÷ 14
= 3

Number of pillows that Dana bought
= 3 x 2 x 6
= 36

(b)
Japheth spent an equal amount of money on the large and small pillows. Make the amount of money spent on the large and small pillows the same.
LCM of 10 and 8 is 40.

Number of large pillows that Japheth bought
= 2 x (40 ÷ 10)
= 2 x 4
= 8

Number of the small pillows that Japheth bought
= 3 x (40 ÷ 8)
= 3 x 5
= 15

Fraction of the pillows that Japheth bought that were small
= ¹⁵_{8 + 15}
= ¹⁵₂₃

Answer(s): (a) 36; (b) ¹⁵₂₃