In order to solve this, we have to formulate two equations, the first one can represent the total acres of the farm, as mentioned in the question, the farm has 500 acres of land allotted for cultivating corn and wheat, then by adding the acres corn and the acres of wheat, x and y, we should get 500, lilke this:
x + y = 500
The Jhonson family can spend as much as $17,600, then by adding the cost of cultivating corn and the cost of cultivating the wheat we should get 17,600, like this:
corn costs + wheat costs = 17,600
The corn and wheat costs are calculated by multiplying the cost per acre cultivated by the number of acres of each product since an acre of corn costs $40 and an acre of wheat costs 28, we can rewrite the above equation to get:
40x + 28y = 17,600
Then, we have two equations
x + y = 500
40x + 28y = 17,600
By solving for y from the first equation, we get:
x + y = 500
x - x + y = 500 - x
y = 500 - x
By replacing 500 - x for y into 40x + 28y = 17,600, we get:
40x + 28y = 17,600
40x + 28(500 - x ) = 17,600
40x + 28×500 - 28x = 17,600
40x - 28x + 28×500 = 17,600
12x + 14,000 = 17,600
12x + 14,000 - 14,000 = 17,600 - 14,000
12x = 3600
x = 3600/12
x = 300
By replacing 300 for x into y = 500 - x, we get:
y = 500 - 300
y = 200
Then, x = 300 and y = 200. This means he should plant 300 acres of corn and 200 acres of wheat.