How can I make a real world problem representing 7.5x=5.5x+25
Fishing boat rental company A costs $7.50 an hour with no initial
fee. Fishing boat rental company B costs only $5.50 an hour but
they charge a $25 initial fee.
I need to know how many hours I would have to rent a fishing boat
so that the charge would be the the same. [If I knew that number
of hours, I would then know that if I wanted to rent a fishing boat
for less than that number of hours, company A would be cheaper, but
if I wanted to rent it for more than that number of hours, company
B would be cheaper.]
Let x = the number of hours when the costs would be the same.
Then the rental cost for company A would be $7.50x and
the rental cost for company B would be $5.50x + $25.
To find the number of hours for which the charge would be the same,
I set those expressions equal:
$7.50x = $5.50x + 25
7.5x = 5.5x + 25
I subtract 5.5x from both sides:
2.0x = 25
x = 25/2
x = 12.5 hours.
So if I wanted to rent the boat for less than 12.5 hours I would
go with rental company A. I would choose rental company B only
if I wanted to rent a fishing boat for more than 12.5 hours.
Edwin