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?
To write a system of linear equations that represents this situation, we need to set up two equations based on the given information.
Let's start with the equation for the total number of acres the farmer wants to plant:
x + y = 180
Next, we know that the farmer wants to plant three times as many acres of corn as wheat. Therefore, the equation for the relationship between corn and wheat is:
x = 3y
By substituting the value of x from the second equation into the first equation, we can solve for y:
3y + y = 180
4y = 180
y = 45
Now, substitute the value of y back into the second equation to find x:
x = 3(45)
x = 135
Therefore, the farmer should plant 135 acres of corn and 45 acres of wheat.
Let's break down the given information step by step:
1. Let's assign the variables x and y to represent the number of acres of corn and wheat planted, respectively.
x: acres of corn planted
y: acres of wheat planted
2. According to the given information, the farmer wants to plant three times as many acres of corn as wheat.
This can be represented by the equation:
x = 3y (Equation 1)
3. The farmer plants a total of 180 acres.
This can be represented by the equation:
x + y = 180 (Equation 2)
To solve this system of linear equations, we can substitute Equation 1 into Equation 2:
3y + y = 180
4y = 180
y = 45
Now, we can substitute the value of y into Equation 1 to find the value of x:
x = 3(45)
x = 135
Therefore, the farmer should plant 135 acres of corn and 45 acres of wheat.
xx + yy = 180
xx = 3 yy
solve the system ... substitution is probably the best approach