PSLE
Jean and Sean bought durians at the prices shown below.

4 Large durians for $9
5 Small durians for $6

1. Jean bought an equal number of large and small durians. She spent $84 more on the large ones. How many durians did she buy altogether?
2. Sean 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 Jean bought is the same. Make the number of large and small durians the same. LCM of 4 and 5 is 20.

Cost of 4 large durians = $9
Cost of 20 large durians = 5 x 9 = $45

Cost of 5 small durians = $6
Cost of 20 small durians = 4 x 6 = $24

Difference in the cost of buying 20 small durians and 20 large durians
= 45 - 24
= $21

Number of sets of durians
= 84 ÷ 21
= 4

Number of durians that Jean bought
= 4 x 2 x 20
= 160

(b)
Sean 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 9 and 6 is 18.

Number of large durians that Sean bought
= 4 x (18 ÷ 9)
= 4 x 2
= 8

Number of the small durians that Sean bought
= 5 x (18 ÷ 6)
= 5 x 3
= 15

Fraction of the durians that Sean bought that were large
= ⁸_{8 + 15}
= ⁸₂₃

Answer(s): (a) 160; (b) ⁸₂₃