one farm is 82 acres larger than another.
together the farms contain 276 acres
how larg is each farm?
solve using two variables and two equations
larger farm --- x acres
smaller farm --- y acres
x-y = 82
x+y = 276
add them, etc
To solve this problem using two variables and two equations, let's define the following variables:
Let x represent the size of the smaller farm in acres.
Let y represent the size of the larger farm in acres.
From the information given, we can set up two equations:
Equation 1: The larger farm is 82 acres larger than the smaller farm.
y = x + 82
Equation 2: Together, the farms contain 276 acres.
x + y = 276
We now have a system of equations. We can solve this system by substituting Equation 1 into Equation 2:
x + (x + 82) = 276
By simplifying the equation:
2x + 82 = 276
2x = 276 - 82
2x = 194
Dividing both sides by 2, we get:
x = 97
Now that we have the value of x, we can substitute it back into Equation 1 to find y:
y = x + 82
y = 97 + 82
y = 179
Therefore, the smaller farm is 97 acres, and the larger farm is 179 acres.