Question

A citrus grower purchased 25 orange trees and 20 grapefruit trees for $290. The next week, at the same prices, the grower bought 20 orange trees and 30 grapefruit trees for $330. Find the cost of an orange tee and the cost of a grapefruit tree.

Answer 1

The cost of an orange tree is $ 6 while that of a grapefruit tree is $

Explanation:

Let x be the cost of an orange tree and y be the cost of a grapefruit tree. In the first week, the citrus grower purchased 25 orange trees and 20 grapefruit trees for $290, so 25x + 20y = 290 (1).

In the next week, the grower bought 20 orange trees and 30 grapefruit trees for $330. So, 20x + 30y = 330 (2)

From (2) y = (330 - 20x)/30 = (33 - 2x)/3

substituting y into (1), we have

25x + 20[(33 - 2x)/3] = 290

multiplying through by 3, we have

75x + 20(33 - 2x) = 870

expanding the bracket, we have

75x + 660 - 40x = 870

collecting like terms, we have

75x - 40x = 870 - 660

35x = 210

dividing both sides by 35, we have

x = 210/35

x = 6

substituting x = 6 into y, we have

y = (33 - 2x)/3

= (33 - 2(6))/3

= (33 - 12)/3

= 21/3

= 7

So the cost of an orange tree is $ 6 while that of a grapefruit tree is $ 7.