Cristian M. answered • 04/08/21
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This is not a differential equations problem. It's a linear model! Nonetheless, let's take a look. I guess I'm going bowling today!
No matter how long Cristian bowls (not very long for me), he has to pay $4. I don't particularly need to know that that is for shoes; I just care that he has to pay this $4 regardless of how long he bowls. This gives us a " + 4 " part for our equation. Now we need to know how much he will pay depending on how long he bowls. He pays $3.50 an hour to bowl. Doesn't it make sense to multiply the number of hours he bowls by the hourly rate? $3.50 to bowl one hour, $7 to bowl two hours, etc. This gives us a "3.50*hours" kind of term to our equation.
Now let's actually build the equation. Let's use some common language to build up to an algebraic equation.
(what Cristian pays in total) = (what he pays based on bowling time) + (a fixed charge to rent shoes, regardless of how long he bowls)
(what he pays in total) = 3.50*(hours bowled) + 4
Let's use y to represent what Cristian pays in total, and let's use x to represent how many hours he bowls. And let's tack on some dollar signs to remind ourselves of what we're dealing with. (They're not necessary, however.)
Our equation is y = $3.50x + $4
Remember that Cristian paid $14.50. Plug this into our new equation, specifically into y (which represents what Cristian paid in total) and solve for x, the number of hours bowled.
(14.50) = 3.50x + 4
Subtract 4 from both sides: 10.50 = 3.50x
Divide both sides by 3.50: 3 = x
Cristian bowled for three hours.
