PSLE
Gem and Flynn bought towels at the prices shown below.

3 Large towels for $8
5 Small towels for $6

1. Gem bought an equal number of large and small towels. She spent $66 more on the large ones. How many towels did she buy altogether?
2. Flynn spent an equal amount of money on the large and small towels. What fraction of the towels he bought were small?

(a)
Number of large and small towels that Gem bought is the same. Make the number of large and small towels the same. LCM of 3 and 5 is 15.

Cost of 3 large towels = $8
Cost of 15 large towels = 5 x 8 = $40

Cost of 5 small towels = $6
Cost of 15 small towels = 3 x 6 = $18

Difference in the cost of buying 15 small towels and 15 large towels
= 40 - 18
= $22

Number of sets of towels
= 66 ÷ 22
= 3

Number of towels that Gem bought
= 3 x 2 x 15
= 90

(b)
Flynn spent an equal amount of money on the large and small towels. Make the amount of money spent on the large and small towels the same.
LCM of 8 and 6 is 24.

Number of large towels that Flynn bought
= 3 x (24 ÷ 8)
= 3 x 3
= 9

Number of the small towels that Flynn bought
= 5 x (24 ÷ 6)
= 5 x 4
= 20

Fraction of the towels that Flynn bought that were small
= ²⁰_{9 + 20}
= ²⁰₂₉

Answer(s): (a) 90; (b) ²⁰₂₉