Cody wants to go on his senior class trip. He finds a job that pays $7 per hour and he also mows lawns for $9 an hour. He needs to earn $693 to pay for the trip, excluding spending money.

Question

Cody wants to go on his senior class trip. He finds a job that pays $7 per hour and he also mows lawns for $9 an hour. He needs to earn $693 to pay for the trip, excluding spending money.

1. Write an inequality describing Cody's goal in terms of hours at his job, x, and hours mowing lawns, y.

2. Graph the inequality. (Scale: 1 box = 11 hrs.)

I know that you can't graph the inequality for me, but if you could maybe walk me through how to do it, or give me a link, I'd really appreciate it.

Answer 1

7x + 9y >= 693

Just graph the line

7x+9y = 693

Now, any x or y value greater than what's on the line will satisfy the inequality, since then 7x+9y will be greater than 693.

Take a look here. The shaded area is all the values of x and y that cause 7x+97 to be at least 693.

http://www.wolframalpha.com/input/?i=solve+7x+%2B+9y+%3E%3D+693

Answer 2

To write an inequality describing Cody's goal, we need to consider the amount he earns from his job and mowing lawns, and compare it to the total amount he needs to pay for the trip.

Let's assume Cody works x hours at his job and y hours mowing lawns. Then, his earnings can be represented as follows:

Earnings from his job = $7 × x
Earnings from mowing lawns = $9 × y

The total amount he needs to earn is $693.

So, the inequality is:

$7x + $9y ≥ $693

To graph this inequality, we need to convert it into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

$7x + $9y ≥ $693
Divide both sides of the inequality by $9 to isolate y:
y ≥ ($693 - $7x) / $9

Now, we can graph the resulting line. However, please note that I am unable to directly create a visual graph. I can provide you with the steps to do it manually or recommend online tools that can help you graph the inequality.

Here is an online graphing tool that you can use:
- Desmos: https://www.desmos.com/calculator

Once you access the tool, enter the inequality in the format y ≥ (693 - 7x) / 9. It will generate the graph for you, representing the solution to Cody's goal.

Remember to set the scale as 1 box = 11 hours, as indicated in the question.