the daily instate entrance fee at indiana state parks is $5

Question

the daily instate entrance fee at indiana state parks is $5 per non commercial vehicle. non commercial vehicles with out of state licenses are charged a daily fee of $7. on a busy day a total of 3170 non commercial vehicles paid an entry fee at one park and the total revenue collected for these fees was $17,890. determine the number of in state and out of state vehicles that visited the park that day

Answer 1

First I will label the total number of in-state vehicles "A" and out-of-state vehicles "B"

On that day the sum of i and o equaled 3170 vehicles. Therefore: 

 

A + B = 3170   

 

We also know that the cost of the vehicle fees in terms of dollars is $5 for A and $7 for B. Therefore for that day: 

5A + 7B= 17890  

 

I'm going to solve for B (get B alone on one side) for each equation: 

 

A + B = 3170    Subtract A from both sides:

-A           -A

 

B= 3170-A

 

Now the second equation: 

5A + 7B= 17890   Subtract 5A from both sides: 

-5A               -5A

 

7B= 17890 - 5A  Divide both sides by 7

/7        /7

 

B=  (17890-5A) / 7

 

Now that both equations equal B, that means they equal each other: 

3170-A=(17890-5A) / 7  Multiply both sides by 7

 

22190-7A = 17890 -5A   Add 7A to both sides

        +7A              +7A

 

22190=17890 +2A   Subtract 17890 from both sides

-17890  -17890 

 

4300 = 2A       Divide both sides by 2

/2         /2 

 

2150 vehicles =A (in-state vehicles)  

 

Now plug it back into the original equation to get B: 

A + B= 3170 

2150 + B= 3170   Subtract 2150 from both sides

-2150          -2150

 

B= 1020 vehicles (out-of-state) 

 

To double check, plug it into the second equation: 

$5(2150) + $7(1020)= $17890

$17890=$17890