# Thread: Inequalities Word Problem

1. ## Inequalities Word Problem

Rondell makes $10 an hour cutting grass and$12 an hour for raking leaves. He cannot work more than 15 hours per week. Graph two inequalities that Rondell can use to determine how many hours he needs to work at each job if he wants to earn at least $120 per week. Ok, so I'm not quite sure on how to set this up... Thanks in advance. 2. Originally Posted by trancefanatic Rondell makes$10 an hour cutting grass and $12 an hour for raking leaves. He cannot work more than 15 hours per week. Graph two inequalities that Rondell can use to determine how many hours he needs to work at each job if he wants to earn at least$120 per week.

Ok, so I'm not quite sure on how to set this up...

Let $x$ be the number of hours he cuts grass
Let $y$ be the number of hours he rakes leaves.

The the amount of makes from cutting grass is $10x$ dollars and the amount of money he makes from raking leaves is $12y$ dollars

He cannot work for more than 15 hours, thus:

$x + y \le 15$

there's your first inequality, simple huh?

he wants the amount of money he makes to be at least (that means "greater than or equal to") 120 dollars, thus:

$10x + 12y \ge 120$

there's your second inequality. that wasn't so bad. now get to graphing, and shade the region that satisfies both inequalities