PSLE
Emily and Reggie bought pillows at the prices shown below.

2 Large pillows for $15
5 Small pillows for $9

1. Emily bought an equal number of large and small pillows. She spent $114 more on the large ones. How many pillows did she buy altogether?
2. Reggie 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 Emily 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 = $15
Cost of 10 large pillows = 5 x 15 = $75

Cost of 5 small pillows = $9
Cost of 10 small pillows = 2 x 9 = $18

Difference in the cost of buying 10 small pillows and 10 large pillows
= 75 - 18
= $57

Number of sets of pillows
= 114 ÷ 57
= 2

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

(b)
Reggie 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 15 and 9 is 45.

Number of large pillows that Reggie bought
= 2 x (45 ÷ 15)
= 2 x 3
= 6

Number of the small pillows that Reggie bought
= 5 x (45 ÷ 9)
= 5 x 5
= 25

Fraction of the pillows that Reggie bought that were small
= ²⁵_{6 + 25}
= ²⁵₃₁

Answer(s): (a) 40; (b) ²⁵₃₁