PSLE
Natalie and Howard bought towels at the prices shown below.

3 Large towels for $15
5 Small towels for $12

1. Natalie bought an equal number of large and small towels. She spent $117 more on the large ones. How many towels did she buy altogether?
2. Howard 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 Natalie 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 = $15
Cost of 15 large towels = 5 x 15 = $75

Cost of 5 small towels = $12
Cost of 15 small towels = 3 x 12 = $36

Difference in the cost of buying 15 small towels and 15 large towels
= 75 - 36
= $39

Number of sets of towels
= 117 ÷ 39
= 3

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

(b)
Howard 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 15 and 12 is 60.

Number of large towels that Howard bought
= 3 x (60 ÷ 15)
= 3 x 4
= 12

Number of the small towels that Howard bought
= 5 x (60 ÷ 12)
= 5 x 5
= 25

Fraction of the towels that Howard bought that were large
= ¹²_{12 + 25}
= ¹²₃₇

Answer(s): (a) 90; (b) ¹²₃₇