I have no idea how to solve this!!please help!

Question

Leland works part time at a car wash and earns $10 an hour. He also babysits and earns $12 an hour.Leland plans to save more than $450 and to work for at most 40 hours in a month?

Write an inequality for each thing he does!

Then graph it

Answer 1

Let h_c be the hours Leland works at the car wash. So the amount he earns at the car wash = 10h_c ($10/hour times the number of hours).

Let h_s be the hours Leland works at sitting. So the amount he earns at babysitting = 12h_s ($12/hour times the number of hours).

The total amount he earns for both jobs is 10h_c + 12h_s and that he plans it to be more than $450. So we can say 10h_c + 12h_s > 450

We are also told that he plans to work "at most" 40 hours so that means h_c + h_s < 40.

We can graph h_c and h_s on a graph with each one being an axis. Let's let h_c be the x-axis and h_s be the y-axis. It might help to build a table.Since the "equal" condition is the boundary for the inequality. We'll build a table for that "equal" condition.

For the amount earned (let 10h_c + 12h_s = 450), the table looks like this:

hc hs amount earned

0 37.5 450

45 0 450

For the hours worked (let h_c + h_s = 40), the table looks like this:

hc hs total hrs worked

0 40 40

40 0 40

Now, graph these and shade the appropriate parts (for the amount earned, we shade above the line because we want the amount earned to be greater than $450. For the number of hours worked, we shade below the line because we want the total hours worked to be less than or equal to 40). We also use a solid line for the hours worked because in can be 40. We use a dotted line for the dollars earned because it cannot be 450 (must be greater than).

Key: Blue represents the hours he needs to earn more than $450. Violet represents the hours worked less than 40. Red is the overlapping area or the hours that will be less than 40 but earn him more than $450.

Answer 2

10x+12y=450

x+y<40