Corey buys some snowboarding equipment for $500, promising to pay $12 a week from part-time earnings until the $500 debt is retired. How many weeks will it take until the outstanding debt is under $100? Write an absolute value inequality that models this situation, and then solve.

Question

mathstudent55 · Answer

He starts by owing $500.
He pays $12 after 1 week, or 12 * 1
He pays $12 after the second week, so now he has paid a total of 12 * 2
He pays $12 after the third week, so now he has paid a total of 12 * 3
etc.
He pays $12 after week x, so now he has paid a total of 12 * x = 12x
Every week, the $500 debt goes down by $12
After x week, his debt is 500 - 12x

anonymous · Answer

Yeah, I got that far. But idk how to do it with absolute value inequalities.

mathstudent55 · Answer

You want the difference between 500 and what he paid to be less than 100,
so you can write
500 - 12x < 100
I agree with you, I don't see why you'd use absolute value here.

anonymous · Answer

Ehhhh I'm not sure. Thanks for helping!