Question

For your summer babysitting jobs you have 10 weeks to work before your family vacation and before you return to school in the fall. You are planning on earning and saving at least $1500 to save for your future car. Mrs. Harris is paying you $8.00 an hour do sit during the day and Mrs. Sanchez is paying you $6.00 per hour to sit in the evening with her child.
Let x = the number of hours you babysit for Mrs. Harris
Let y = the number of hours you babysit for Mrs. Sanchez
1. Write an inequality describing the number of hours you want to work each week to reach your summer goal of $1500. Remem

Answer 1

Let's start with Mrs. Harris.
She pays $8.00 per hour.

In 1 hour, you earn $8 * 1
In 2 hours, you earn $8 * 2
In 3 hours, you earn $8 * 3
In x hours, how much do you earn?

Answer 2

you have 10 weeks to work. How much do you want to average per week? 2. Graph this inequality and shade the area that includes all the solutions to your inequality.

3. What is the boundary line? Is it a solid or dotted line? Why?

4. You cannot work more than 25 hours each week. How could you denote this on your graph?

5. You cannot work more than 25 hours a week. Give 3 reasonable solutions using your graph for the number of hours you could work for Mrs. Harris and Mrs. Sanchez, and not exceed 25 hours a week. Use words and symbols to explain how you determined your answer.

Answer 3

i've already done the first answer.. but i dont know how to do the rest .-.

Answer 4

What did you get for the first answer?

Answer 5

10(x*8 + y*6) ≥ 1500
80x + 60y ≥ 1500

per week:

8x + 6y ≥ 150

Answer 6

Great.
You can simplify it by dividing the entire equation by 2.

Answer 7

okk

Answer 8

That is the amount you earn per week. That is part 1.
Since there are 10 weeks, and you want to earn a total of at least $1500, you want to earn an average of at least $1500/10 per week, or at least $150 per week.

Answer 9

Now you need to graph it.

Answer 10

8x + 6y ≥ 150
4x + 3y ≥ 75

Do you know how to graph an inequality?

Answer 11

no.. like i somewhat know it, but im not too familiar with it. i just started doing themm

Answer 12

Ok. Start by looking at the corresponding equation. All you do is replace the \(\ge\) symbol with = in the inequality

Now graph that line.

Answer 13

In other words, to plot
4x + 3y ≥ 75,
first plot
4x + 3y = 75

Answer 14

oh okay :)

Answer 15

Ok. Now since the inequality symbol is \(\le\) or \(\ge\) and not simply < or >, the line is drawn as a solid line.

Answer 16

You should have this so far.

Answer 17

ok, and do i shade above?

Answer 18

Right.
The way you find which side to shade is you chose a point on either side of the line.
Then you test that point on the original inequality. If the point makes the inequality true you shade the entire half-plane the point is in. If the point does not work in the inequality, then shade the other half plane.

Answer 19

An easy point to test with is (0, 0).

Test (0, 0) in
4x + 3y ≥ 75

4(0) + 3(0) ≥ 75
0 + 0 ≥ 75
0 ≥ 75 is a false statement, so (0, 0) does not work and the entire half plane it lies in does not work either, so you choose the other half plane.

Answer 20

That's what the graph looks like.

Answer 21

I added the number 25 to the x axis.