PSLE
Betty and Caden bought pillows at the prices shown below.

2 Large pillows for $10
5 Small pillows for $4

1. Betty bought an equal number of large and small pillows. She spent $84 more on the large ones. How many pillows did she buy altogether?
2. Caden 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 Betty bought is the same. Make the number of large and small pillows the same. LCM of 2 and 5 is 10.

Cost of 2 large pillows = $10
Cost of 10 large pillows = 5 x 10 = $50

Cost of 5 small pillows = $4
Cost of 10 small pillows = 2 x 4 = $8

Difference in the cost of buying 10 small pillows and 10 large pillows
= 50 - 8
= $42

Number of sets of pillows
= 84 ÷ 42
= 2

Number of pillows that Betty bought
= 2 x 2 x 10
= 40

(b)
Caden 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 4 is 20.

Number of large pillows that Caden bought
= 2 x (20 ÷ 10)
= 2 x 2
= 4

Number of the small pillows that Caden bought
= 5 x (20 ÷ 4)
= 5 x 5
= 25

Fraction of the pillows that Caden bought that were large
= ⁴_{4 + 25}
= ⁴₂₉

Answer(s): (a) 40; (b) ⁴₂₉