PSLE
Zoe and Luis bought durians at the prices shown below.

4 Large durians for $12
7 Small durians for $8

1. Zoe bought an equal number of large and small durians. She spent $208 more on the large ones. How many durians did she buy altogether?
2. Luis 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 Zoe bought is the same. Make the number of large and small durians the same. LCM of 4 and 7 is 28.

Cost of 4 large durians = $12
Cost of 28 large durians = 7 x 12 = $84

Cost of 7 small durians = $8
Cost of 28 small durians = 4 x 8 = $32

Difference in the cost of buying 28 small durians and 28 large durians
= 84 - 32
= $52

Number of sets of durians
= 208 ÷ 52
= 4

Number of durians that Zoe bought
= 4 x 2 x 28
= 224

(b)
Luis 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 8 is 24.

Number of large durians that Luis bought
= 4 x (24 ÷ 12)
= 4 x 2
= 8

Number of the small durians that Luis bought
= 7 x (24 ÷ 8)
= 7 x 3
= 21

Fraction of the durians that Luis bought that were small
= ²¹_{8 + 21}
= ²¹₂₉

Answer(s): (a) 224; (b) ²¹₂₉