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Question 1041152: Your friend Alex has won a scholarship to study abroad. Alex has only 8 weeks to earn enough money to buy a plane ticket, and he wants to work at an amusement park or a tech internship over the summer to achieve this goal. His plane ticket cost $2,200. The tech internship is part time 20 hr/wk with $11.50/hr, where as the amusement park is full-time 40hr/wk with $9/hr+$100 bonus when he starts. You want to find the income line that represents how much Alex makes, where
x = hours worked
y = money earned
How much time does Alex have? For each job, use information from the table to calculate the number of hours Alex could work before he has to buy his plane ticket.
what is the slope and y intercept (x,y) of both these work places.
For each job, write an inequality that represents the number of hours Alex could work before the trip.
Write an inequality that represents the amount of money Alex needs to earn. PLEASE HELP IM SO LOST
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! He needs to earn the same or more than 2200, so the inequality will be >=2200
For job A at 11.50/hr*20 hours/week*8 weeks = $230*8=$1840. I am not clear why this is an inequality. We know the wage, the number of hours per week and the number of weeks. It is sufficient to calculate how much money he will make in 8 weeks. If one wants an inequality, I have it below, which is how many hours he must work in order to buy the ticket. If this is a graph, the slope is change in y over change in x. This is money earned/hours worked, or money/hour. The slope is $11.50/hour, his wage. The intercept is 0, meaning at 0 hours worked, he has no money.
The inequality is 11.50/hr*20 hours/week*z weeks >=2200. That is $230 z >=$2200. That is 9.565 weeks or 10 weeks rounding up to the higher number of weeks,
divide both sides by 11.50 and x>=191.30 or x>=192 hours, rounding to the upper hour. He is working 20 hours a week, so that isn't enough. That is another way of saying it is 9.565 weeks.
For the amusement park, it is $100+$9/hour*40 hr/week*8 weeks. There isn't an inequality here. It is equal to $100+$360*8=$2980. It is more than enough. The slope of this is $9/hour, and the y-intercept is $100, meaning at 0 hours he has $100, because he gets a bonus when he starts.
The inequality for the second job is $100*$9/hour*40hr/week*z weeks>=$2200
That is $9/hour*40 hours/week*z weeks >=$2100, subtracting $100 from each side.
360z>=2100
z>=5.833 weeks or 6 if one round to the higher week.
The line on the left has an intercept at y=100, and before 8 weeks, it crosses the y=$2200 line.
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