word problem

Question

the two stadiums with the largest capacities are Marshfield Stadium and Bowden stadium. Marshfield Stadium has a capacity of 5,067 more than Bowden. If the combined capacity for the two stadiums is 210,355, find the capacity for each stadium.

Answer 1

Let's assign the following variables....

B=Bowden Stadium

M=Marshfield Stadium

 

And write the following equations from

the problem statement....

    M=B+5067.......Eq1, given

M+B=210,355......Eq2, given

 

Substitute Eq1 into Eq2...

            M+B=210,355...Eq2

(B+5067)+B=210,355...substitute for "M"

     2B+5067=210,355...simplify

               2B=205,288....subtract 5067, both sides

             ∴ B=102,644....divide both sides by 2

 

Substitute the value for "B" into Eq2...

                  M=B+5067....Eq1, given

  M+102,355=210,355...substitute for "B"

              ∴ M=107,711...subtract 102,355,

                                         both sides

 

Now let's check by substituting both calculated values into Eq1 and Eq2 and simplifying...

         M=B+5067.....................Eq1

107,711=102,644+5067........substitute for "M, B"

107,711=107,711...................true, √check

 

                   M+B=210,355......Eq2

107,711+102,644=210,355...substitute for "M, B"

              210,355=210,355.....true, √check

 

Our calculated values are correct.  So the capacities of each stadium are...

Bowden Stadium........102,644 fans

Marshfield Stadium...107,711 fans

 

Always check your solutions and work!