Question

A farmer plants corn and wheat on a 180-acre farm. the farmer wants to plant three times as many acres of corn as wheat. write a system of linear equations that represents this situation. use xx to represent the number of aces of corn planted and yy to represent the number of acres of wheat planted. how many acres of each crop should the farmer plant?

Answer 1

The farmer should plant 135 acres of corn and 45 acres of wheat.

Step-by-step explanation:

To represent the situation in a system of linear equations, we need to define the number of acres of corn planted (x) and the number of acres of wheat planted (y). Given that the farmer wants to plant three times as many acres of corn as wheat and the total farm size is 180 acres, we can set up the following system of linear equations:

x = 3y

x + y = 180

Solving this system of equations, we can find the values of x and y. Substituting the value of x from the first equation into the second equation, we get:

3y + y = 180

4y = 180

y = 45

Substituting the value of y back into the first equation, we can find the value of x:

x = 3(45) = 135

Therefore, the farmer should plant 135 acres of corn and 45 acres of wheat.

Answer 2

Let the number of corn acres be xx and the number of wheat acres be yy.
We are given that:
1- The total number of acres is 180, this means that:
xx + yy = 180 ..............> equation I
2- The number of corn acres is 3 times that of wheat. This means that:
xx = 3yy .........> equation II

Substitute with equation II in equation I to get the value of yy as follows:
xx + yy = 180
3yy + yy = 180
4yy = 180
yy = 45 acres

Now substitute with yy in equation II to get xx as follows:
xx = 3yy
xx = 3*45
xx = 135 acres

Based on the above calculations:
acres of corn = xx = 135 acres
acres of wheat = yy = 45 acres