PSLE
Hazel and Mark bought towels at the prices shown below.

4 Large towels for $10
5 Small towels for $8

1. Hazel bought an equal number of large and small towels. She spent $54 more on the large ones. How many towels did she buy altogether?
2. Mark 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 Hazel 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 = $10
Cost of 20 large towels = 5 x 10 = $50

Cost of 5 small towels = $8
Cost of 20 small towels = 4 x 8 = $32

Difference in the cost of buying 20 small towels and 20 large towels
= 50 - 32
= $18

Number of sets of towels
= 54 ÷ 18
= 3

Number of towels that Hazel bought
= 3 x 2 x 20
= 120

(b)
Mark 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 10 and 8 is 40.

Number of large towels that Mark bought
= 4 x (40 ÷ 10)
= 4 x 4
= 16

Number of the small towels that Mark bought
= 5 x (40 ÷ 8)
= 5 x 5
= 25

Fraction of the towels that Mark bought that were large
= ¹⁶_{16 + 25}
= ¹⁶₄₁

Answer(s): (a) 120; (b) ¹⁶₄₁