PSLE
Ivory and Ethan bought mangoes at the prices shown below.

2 Large mangoes for $15
3 Small mangoes for $10

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

(a)
Number of large and small mangoes that Ivory bought is the same. Make the number of large and small mangoes the same. LCM of 2 and 3 is 6.

Cost of 2 large mangoes = $15
Cost of 6 large mangoes = 3 x 15 = $45

Cost of 3 small mangoes = $10
Cost of 6 small mangoes = 2 x 10 = $20

Difference in the cost of buying 6 small mangoes and 6 large mangoes
= 45 - 20
= $25

Number of sets of mangoes
= 75 ÷ 25
= 3

Number of mangoes that Ivory bought
= 3 x 2 x 6
= 36

(b)
Ethan spent an equal amount of money on the large and small mangoes. Make the amount of money spent on the large and small mangoes the same.
LCM of 15 and 10 is 30.

Number of large mangoes that Ethan bought
= 2 x (30 ÷ 15)
= 2 x 2
= 4

Number of the small mangoes that Ethan bought
= 3 x (30 ÷ 10)
= 3 x 3
= 9

Fraction of the mangoes that Ethan bought that were small
= ⁹_{4 + 9}
= ⁹₁₃

Answer(s): (a) 36; (b) ⁹₁₃