PSLE
Zara and Asher bought mangoes at the prices shown below.

4 Large mangoes for $15
7 Small mangoes for $9

1. Zara bought an equal number of large and small mangoes. She spent $138 more on the large ones. How many mangoes did she buy altogether?
2. Asher spent an equal amount of money on the large and small mangoes. What fraction of the mangoes he bought were large?

(a)
Number of large and small mangoes that Zara bought is the same. Make the number of large and small mangoes the same. LCM of 4 and 7 is 28.

Cost of 4 large mangoes = $15
Cost of 28 large mangoes = 7 x 15 = $105

Cost of 7 small mangoes = $9
Cost of 28 small mangoes = 4 x 9 = $36

Difference in the cost of buying 28 small mangoes and 28 large mangoes
= 105 - 36
= $69

Number of sets of mangoes
= 138 ÷ 69
= 2

Number of mangoes that Zara bought
= 2 x 2 x 28
= 112

(b)
Asher 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 9 is 45.

Number of large mangoes that Asher bought
= 4 x (45 ÷ 15)
= 4 x 3
= 12

Number of the small mangoes that Asher bought
= 7 x (45 ÷ 9)
= 7 x 5
= 35

Fraction of the mangoes that Asher bought that were large
= ¹²_{12 + 35}
= ¹²₄₇

Answer(s): (a) 112; (b) ¹²₄₇