PSLE
Erika and Gabriel bought towels at the prices shown below.

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

1. Erika bought an equal number of large and small towels. She spent $152 more on the large ones. How many towels did she buy altogether?
2. Gabriel 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 Erika 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 = $10
Cost of 15 large towels = 5 x 10 = $50

Cost of 5 small towels = $4
Cost of 15 small towels = 3 x 4 = $12

Difference in the cost of buying 15 small towels and 15 large towels
= 50 - 12
= $38

Number of sets of towels
= 152 ÷ 38
= 4

Number of towels that Erika bought
= 4 x 2 x 15
= 120

(b)
Gabriel 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 4 is 20.

Number of large towels that Gabriel bought
= 3 x (20 ÷ 10)
= 3 x 2
= 6

Number of the small towels that Gabriel bought
= 5 x (20 ÷ 4)
= 5 x 5
= 25

Fraction of the towels that Gabriel bought that were small
= ²⁵_{6 + 25}
= ²⁵₃₁

Answer(s): (a) 120; (b) ²⁵₃₁