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

4 Large towels for $18
5 Small towels for $12

1. Xandra bought an equal number of large and small towels. She spent $168 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 large?

(a)
Number of large and small towels that Xandra bought is the same. Make the number of large and small towels the same. LCM of 4 and 5 is 20.

Cost of 4 large towels = $18
Cost of 20 large towels = 5 x 18 = $90

Cost of 5 small towels = $12
Cost of 20 small towels = 4 x 12 = $48

Difference in the cost of buying 20 small towels and 20 large towels
= 90 - 48
= $42

Number of sets of towels
= 168 ÷ 42
= 4

Number of towels that Xandra bought
= 4 x 2 x 20
= 160

(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 18 and 12 is 36.

Number of large towels that Flynn bought
= 4 x (36 ÷ 18)
= 4 x 2
= 8

Number of the small towels that Flynn bought
= 5 x (36 ÷ 12)
= 5 x 3
= 15

Fraction of the towels that Flynn bought that were large
= ⁸_{8 + 15}
= ⁸₂₃

Answer(s): (a) 160; (b) ⁸₂₃