Linear equation

Question

Petroleum rights to 140 acres of land are leased for 37000. Part of the land leases for $200 per acre, and the reminder for $300 per acre. How much is leased at each price?

Answer 1

x = number of acres at $200

(140-x) = number of acres at $300

200x + 300(140-x) = 37000

-100x +42000=37000

5000 = 100x

50 = x acres at $200

(140-x) = 90 acres at $300

Answer 2

Let x acres be the land leased for $200/acre

Let y acres be the land leased for $300/acre

 

x+y=140                                         (1)

(200*x) + (300*y) = 37000               (2)

 

solve (1) and (2) linearly

 

(200*x) + (200*y) = 28000               (3)

 

Subtracting (3) from (2)

(200*x) + (300*y) = 37000

-(200*x) - (200*y) = -28000

 

100*y = 9000

y = 90 acres

so x = 50 acres