PSLE
Vanessa and Japheth bought towels at the prices shown below.

2 Large towels for $15
5 Small towels for $10

1. Vanessa bought an equal number of large and small towels. She spent $110 more on the large ones. How many towels did she buy altogether?
2. Japheth 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 Vanessa bought is the same. Make the number of large and small towels the same. LCM of 2 and 5 is 10.

Cost of 2 large towels = $15
Cost of 10 large towels = 5 x 15 = $75

Cost of 5 small towels = $10
Cost of 10 small towels = 2 x 10 = $20

Difference in the cost of buying 10 small towels and 10 large towels
= 75 - 20
= $55

Number of sets of towels
= 110 ÷ 55
= 2

Number of towels that Vanessa bought
= 2 x 2 x 10
= 40

(b)
Japheth 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 10 is 30.

Number of large towels that Japheth bought
= 2 x (30 ÷ 15)
= 2 x 2
= 4

Number of the small towels that Japheth bought
= 5 x (30 ÷ 10)
= 5 x 3
= 15

Fraction of the towels that Japheth bought that were large
= ⁴_{4 + 15}
= ⁴₁₉

Answer(s): (a) 40; (b) ⁴₁₉