PSLE
Xuan and Fred bought towels at the prices shown below.

2 Large towels for $9
3 Small towels for $7

1. Xuan bought an equal number of large and small towels. She spent $39 more on the large ones. How many towels did she buy altogether?
2. Fred 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 Xuan bought is the same. Make the number of large and small towels the same. LCM of 2 and 3 is 6.

Cost of 2 large towels = $9
Cost of 6 large towels = 3 x 9 = $27

Cost of 3 small towels = $7
Cost of 6 small towels = 2 x 7 = $14

Difference in the cost of buying 6 small towels and 6 large towels
= 27 - 14
= $13

Number of sets of towels
= 39 ÷ 13
= 3

Number of towels that Xuan bought
= 3 x 2 x 6
= 36

(b)
Fred 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 9 and 7 is 63.

Number of large towels that Fred bought
= 2 x (63 ÷ 9)
= 2 x 7
= 14

Number of the small towels that Fred bought
= 3 x (63 ÷ 7)
= 3 x 9
= 27

Fraction of the towels that Fred bought that were large
= ¹⁴_{14 + 27}
= ¹⁴₄₁

Answer(s): (a) 36; (b) ¹⁴₄₁