Please help,algebra word problem,makin me crazy :(

Question

The governor of state B earns $51,000 more than the governor of state A. The governor of state C earns $80,000 less than twice the governor of state A. If the total of all three salaries is $465,000, find the salaries.?????

Answer 1

I like the enthusiasm. XD

 

So first thing I would do here (for any problem actually) is write down what is given to me in a mathematical way, you'll see what I mean.

 

first Gov. of State B earns 51,000 more than gov. of state A so I would write B = 51,000 +A

Next it says gov of state C earns 80,000 less than twice of gov. of state A, so I write: C = 2A - 80,000

Finally, the total of all 3 is 465,000: A + B +C = 465,000

 

 

To solve this problem we first need to get one equation down to 1 variable. To do this notice that the first 2 equations both have only the variable A on the right hand side. Therefore, substituting the first two equations into the lat one will give you an equation with only 1 variable:

 

A + (51,000 +A) + (2A -80,000) = 465,000

 

solving this will give you the value for A. Once you have the value for A getting B and C is just a matter of plugging in. 

Answer 2

Just translate:

 

  "The governor of state B earns $51,000 more than the governor of state A"    means

                                   B    =    $51,000       +                                   A                      [eq1]

 

  "The governor of state C earns $80,000 less than twice the governor of state A"      means

                                   C     =         - $80,000      +  2*A                    [eq2]

 

  "the total of all three salaries is $465,000"    means    A + B + C = $465,000     [eq3\

 

Re-write:

        A    -     B                  =  -$51,000              [from eq1]

       2A               -    C       =   $80,000              [from eq2]

        A    +    B    +   C      =  $465,000               [eq3 again]

 ------------------------------------------------      [add equations; this is Elimination Method]

      4A                              = $494,000

        A                             = $123,500             [eq4]

        A    -     B                  =  -$51,000              [from eq1]

  ---------------------------------------------        [subtract equations]

               +   B                 = $174,500

 

       2A                            = $247,000            [from eq4]

       2A                   -  C    =   $80,000           [from eq2]

  ---------------------------------------------       [subtract equations]

                                 C    = $167,000

 

Check:

   Is     $174,500  =   $51,000 + $123,500   ?

             $174,500 = $174,500   ?yes

   Is    $167,000 = 2*$123,000 - $80,000   ?

          $167,000 = $246,000 - $80,000   ?

           $167,000 = $167,000   ?yes

   Is   $123,500 + $174,500 + $167,000 = $465,000   ?

            $465,000 = $465,000   ?yes

Answer 3

Hi Angela, let a represent the governor of State A's income. Let b represent the governor of State B's income. Let c represent the governor of State C's income.

 

Equation:

 

a + b + c = 465000

 

But

 

b = a + 51000

 

and 

 

c = 2a - 80000

 

Substitute

 

a + (a + 51000) + (2a - 80000) = 465000

 

Combine terms:

 

4a - 29000 = 465000

 

Add 29000 to both sides:

 

4a = 494000

 

Divide by 4:

 

a = 123500

 

The governor of State A earns $123,500.

 

The governor of State B earns A + 51000, or 174,500.

 

The governor of State C earns 2 * A - 8000, or 167,000.

 

Check:

 

123,500 + 174,500 + 167,000 = 465,000

 

465,000 = 465, 000

 

Values check.

 

Questions?