PSLE
Betty and Zeph bought durians at the prices shown below.

3 Large durians for $12
5 Small durians for $6

1. Betty bought an equal number of large and small durians. She spent $126 more on the large ones. How many durians did she buy altogether?
2. Zeph spent an equal amount of money on the large and small durians. What fraction of the durians he bought were small?

(a)
Number of large and small durians that Betty bought is the same. Make the number of large and small durians the same. LCM of 3 and 5 is 15.

Cost of 3 large durians = $12
Cost of 15 large durians = 5 x 12 = $60

Cost of 5 small durians = $6
Cost of 15 small durians = 3 x 6 = $18

Difference in the cost of buying 15 small durians and 15 large durians
= 60 - 18
= $42

Number of sets of durians
= 126 ÷ 42
= 3

Number of durians that Betty bought
= 3 x 2 x 15
= 90

(b)
Zeph 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 12 and 6 is 12.

Number of large durians that Zeph bought
= 3 x (12 ÷ 12)
= 3 x 1
= 3

Number of the small durians that Zeph bought
= 5 x (12 ÷ 6)
= 5 x 2
= 10

Fraction of the durians that Zeph bought that were small
= ¹⁰_{3 + 10}
= ¹⁰₁₃

Answer(s): (a) 90; (b) ¹⁰₁₃