PSLE
Rachel and Lee bought durians at the prices shown below.

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

1. Rachel bought an equal number of large and small durians. She spent $75 more on the large ones. How many durians did she buy altogether?
2. Lee spent an equal amount of money on the large and small durians. What fraction of the durians he bought were large?

(a)
Number of large and small durians that Rachel bought is the same. Make the number of large and small durians the same. LCM of 3 and 4 is 12.

Cost of 3 large durians = $10
Cost of 12 large durians = 4 x 10 = $40

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

Difference in the cost of buying 12 small durians and 12 large durians
= 40 - 15
= $25

Number of sets of durians
= 75 ÷ 25
= 3

Number of durians that Rachel bought
= 3 x 2 x 12
= 72

(b)
Lee spent an equal amount of money on the large and small durians.  Make the amount of money spent on the large and small durians the same.
LCM of 10 and 5 is 10.

Number of large durians that Lee bought
= 3 x (10 ÷ 10)
= 3 x 1
= 3

Number of the small durians that Lee bought
= 4 x (10 ÷ 5)
= 4 x 2
= 8

Fraction of the durians that Lee bought that were large
= ³_{3 + 8}
= ³₁₁

Answer(s): (a) 72; (b) ³₁₁