area of a certain state (state1) five times the area of another state(state2). If the sum of their area is 6,000,000 square miles, find area of each state
x+5x = 6million mi^2
x = 1million mi^2
So, to make sure I understand you,
State 1 is 5million
State 2 is 1million
To find the area of each state, let's assign variables. Let A1 represent the area of state1, and A2 represent the area of state2.
We're given that the area of state1 is five times the area of state2. Mathematically, this can be expressed as:
A1 = 5A2 (Equation 1)
We're also given that the sum of their areas is 6,000,000 square miles. Mathematically, this can be expressed as:
A1 + A2 = 6,000,000 (Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2) with two unknowns (A1 and A2). We can use substitution or elimination method to solve the system.
Let's solve it using substitution:
We rearrange Equation 1 to express A2 in terms of A1:
A2 = A1/5
Substitute this value of A2 in Equation 2:
A1 + (A1/5) = 6,000,000
Multiply throughout by 5 to remove the fraction:
5A1 + A1 = 30,000,000
6A1 = 30,000,000
A1 = 30,000,000 / 6
A1 = 5,000,000
Now substitute the value of A1 into Equation 1 to find A2:
A2 = 5A1 = 5 * 5,000,000 = 25,000,000
Therefore, the area of state1 (A1) is 5,000,000 square miles, and the area of state2 (A2) is 25,000,000 square miles.