PSLE
Kathy and Dylan bought pillows at the prices shown below.

2 Large pillows for $9
3 Small pillows for $6

1. Kathy bought an equal number of large and small pillows. She spent $30 more on the large ones. How many pillows did she buy altogether?
2. Dylan spent an equal amount of money on the large and small pillows. What fraction of the pillows he bought were large?

(a)
Number of large and small pillows that Kathy 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 = $9
Cost of 6 large pillows = 3 x 9 = $27

Cost of 3 small pillows = $6
Cost of 6 small pillows = 2 x 6 = $12

Difference in the cost of buying 6 small pillows and 6 large pillows
= 27 - 12
= $15

Number of sets of pillows
= 30 ÷ 15
= 2

Number of pillows that Kathy bought
= 2 x 2 x 6
= 24

(b)
Dylan 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 9 and 6 is 18.

Number of large pillows that Dylan bought
= 2 x (18 ÷ 9)
= 2 x 2
= 4

Number of the small pillows that Dylan bought
= 3 x (18 ÷ 6)
= 3 x 3
= 9

Fraction of the pillows that Dylan bought that were large
= ⁴_{4 + 9}
= ⁴₁₃

Answer(s): (a) 24; (b) ⁴₁₃