PSLE
Gwen and Zane bought mangoes at the prices shown below.

4 Large mangoes for $15
5 Small mangoes for $10

1. Gwen bought an equal number of large and small mangoes. She spent $105 more on the large ones. How many mangoes did she buy altogether?
2. Zane 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 Gwen bought is the same. Make the number of large and small mangoes the same. LCM of 4 and 5 is 20.

Cost of 4 large mangoes = $15
Cost of 20 large mangoes = 5 x 15 = $75

Cost of 5 small mangoes = $10
Cost of 20 small mangoes = 4 x 10 = $40

Difference in the cost of buying 20 small mangoes and 20 large mangoes
= 75 - 40
= $35

Number of sets of mangoes
= 105 ÷ 35
= 3

Number of mangoes that Gwen bought
= 3 x 2 x 20
= 120

(b)
Zane 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 Zane bought
= 4 x (30 ÷ 15)
= 4 x 2
= 8

Number of the small mangoes that Zane bought
= 5 x (30 ÷ 10)
= 5 x 3
= 15

Fraction of the mangoes that Zane bought that were small
= ¹⁵_{8 + 15}
= ¹⁵₂₃

Answer(s): (a) 120; (b) ¹⁵₂₃