The combined area of New York and California is 204,192 square miles. The area of California is 108,530 square miles more than that of New York. Find the land area of each state.
CA,
mi2
NY,
mi2
.
Let x = the area of New York.
x + x + 108,530 = 204,192
To find the land area of each state, we can set up a system of equations based on the information given. Let's denote the land area of California as CA and the land area of New York as NY.
From the problem statement, we know that the combined area of New York and California is 204,192 square miles:
CA + NY = 204,192
We are also given that the area of California is 108,530 square miles more than that of New York:
CA = NY + 108,530
Now we have a system of two equations:
CA + NY = 204,192
CA = NY + 108,530
To solve this system, we can substitute the second equation into the first equation:
(NY + 108,530) + NY = 204,192
Combining like terms:
2NY + 108,530 = 204,192
Subtracting 108,530 from both sides:
2NY = 95,662
Dividing both sides by 2:
NY = 47,831
Now that we have the value for NY, we can substitute it back into one of the equations to find CA:
CA = NY + 108,530
CA = 47,831 + 108,530
CA = 156,361
Therefore, the land area of California is 156,361 square miles, and the land area of New York is 47,831 square miles.