Write an equation for the following situation.
Polly Gone has $120 saved already. She wants to save for airfare to visit her friend. The airfare will cost $500 and she can save $60 per week. How many weeks will it take her to save enough money for the airfare?
(Hint: The goal is to write the equation so that it models the situation, not to solve it!)
Equation that solves the problem: (500-120)/60=x
Equation that models the problem: ??????????
Time needed = (500-120)/60
What's with all this "model the problem" stuff.
You make a statement such as
Time needed = (500-120)/60
work it out, and you are done.
You had that, good job
Introducing variables like x is not necessary, and asking for an "equation" results in abuse of the concept of equations.
It is this unnecessary complication of a simple arithmetic problem that must drive students crazy (and I hope most teachers)
Sorry about the rant.
To model the problem, we can use the equation:
120 + 60x = 500
Explanation:
The equation represents the total amount of money that Polly will have after x weeks of saving.
Starting with her initial savings of $120, she will save an additional $60 per week. So, after x weeks, she will have saved a total of 60x dollars.
To be able to afford the airfare, the total amount she has saved (120 + 60x) needs to be equal to or greater than $500.
Thus, the equation is 120 + 60x = 500. This equation models the situation and can be used to find the number of weeks (x) it will take her to save enough money for the airfare.