The two stadiums with the largest capacities are Marshfield Stadium and Bowden Stadium. The capacity of Marshfield Stadium exceeds that of Bowden by 7,341 people. Combined, the two stadiums have a capacity of 210,355 people. Find the capacity of each stadium.
Marshfield Stadium-
Bowden Stadium-
I need help with this one please.
Let's assume the capacity of Bowden Stadium is x.
According to the information given, the capacity of Marshfield Stadium exceeds that of Bowden by 7,341 people. So, the capacity of Marshfield Stadium can be expressed as (x + 7,341).
Combined, the two stadiums have a capacity of 210,355 people. So, we can set up the following equation:
x + (x + 7,341) = 210,355
Simplifying the equation gives us:
2x + 7,341 = 210,355
Subtracting 7,341 from both sides:
2x = 203,014
Dividing both sides by 2:
x = 101,507
So, the capacity of Bowden Stadium is 101,507 people.
And the capacity of Marshfield Stadium is x + 7,341 = 101,507 + 7,341 = 108,848 people.
To find the capacity of each stadium, let's set up a system of equations based on the given information.
Let's assume the capacity of Marshfield Stadium is represented by 'M', and the capacity of Bowden Stadium is represented by 'B'.
From the first statement, we know that the capacity of Marshfield Stadium exceeds that of Bowden by 7,341 people. So we can write the equation:
M = B + 7,341
The second statement tells us that the combined capacity of both stadiums is 210,355 people. So we can write another equation:
M + B = 210,355
Now we have a system of two equations that we can solve simultaneously to find the capacities of Marshfield Stadium and Bowden Stadium.
We can use the substitution method to solve this system of equations. Since we already have an equation for M in terms of B, we can substitute M in the second equation with B + 7,341:
(B + 7,341) + B = 210,355
Simplifying the equation:
2B + 7,341 = 210,355
Subtracting 7,341 from both sides:
2B = 203,014
Dividing both sides by 2:
B = 101,507
Now we know the capacity of Bowden Stadium is 101,507.
To find the capacity of Marshfield Stadium, we substitute this value of B back into our equation for M:
M = B + 7,341
M = 101,507 + 7,341
M = 108,848
Therefore, the capacity of Marshfield Stadium is 108,848.
To summarize:
Marshfield Stadium's capacity is 108,848.
Bowden Stadium's capacity is 101,507.
B = Bowden
2B + 7341 = 210,355
Solve for B.