(NEED ASAP!!) Algebra Word Problem

Question

You have been offered two different jobs. Job A would pay you $12 an hour but a bonus at the end of the month of $100. Job B would pay you $16 an hour but would have no bonus offered.

Write an equation that represents the pay for each job offer.

How would you graph this using the the system of equations?

What job would you decide to take to make the most money and explain your reasoning?

Answer 1

Hello!

So to start solving this we are going to have to start by defining some terms that we are looking for, and the variables we will use to represent them.

I will be using x to be the number of hours worked at each job, and y will represent the income. I am going to jump to the answer for Job A and explain my reasoning after:

Y_a= 12(x_a) + 100

In this instance, Y_a represents the amount of money you would make per month in Job A. While x_a represents the number of hours you are working per month. We multiply the number of hours you work per month (x_a) by 12 because that is your hourly wage for Job A. Then, we add 100 to the end of the equation because that represent your bonus that you receive at the end of the month (presumably because you work hard and are good at your job, yay!)

Now we will be using this same logic to create an equation for Job B. We will use the same steps, except this time we wont plug in anything for a bonus.

Y_b = 16(x_b)

This is our FULL equation for the amount of money you would make at Job B, per month.

Let's compare these two in a system of equations:

For Job A: Y = 12x + 100

For Job B: Y = 16x

I removed the subscripts to make it easier to compare them. This are our two equations for the two job offers you received!

Now moving on to the graphs:

We know the Y-intercept for the first function (Job A) is at (0,100). This means that even if you worked 0 hours for the entire month, you would still make the 100 dollars from your bonus!

Whereas for Job B, the Y-intercept is at (0,0). This makes sense because you dont have any bonuses and so if you worked 0 hours, you would make 0 dollars.

Next we will use this system of equations we found above. We want to find in what scenario would we be making the same amount working either job. So to do that we set the two equations equal to eachother.

12x+100 = 16x

100 = 16x - 12x

100 = 4x

x = 25

This means that if you worked 25 hours for the entire month, you would be making the same at either job. To find what that amount is, we simply need to put 25 in for x in either equation (remember that it will be the same in this case because we set the equations equal to eachother). Doing this would put you at making 400 dollars that month!

Because these are linear functions (that means they are a straigh line), we can just connect the dots to get the two graphs of the functions. So connect our first function from (0,100) to (25,400) remember to go a little past this because you could work more than 25 hours. Do the same for Job B and connect (0,0) to (25,400).

This will get you the graphs of the two functions!

Now here comes the real question! Which job should you take?

This depends on how many hours you will be working! If you are working less than 25 hours a month, you should take Job A. If you will be working more than 25 hours a month, you should take Job B. Considering the fact that almost every job requires you to work more than 25 hours a month (most require you to work more than that a week!), it is a safe bet to assume that you should take Job B as you will make more money in the long run.

Hope that answers your question! Let me know if you have any follow ups!

Answer 2

Hello Olivia,

Let x represents the number of hours worked per month, and y represents the monthly payment (in dollars).

Write an equation that represents the pay for each job offer.

Job A:

y = 12 x + 100

Job B:

y = 16 x

How would you graph this using the the system of equations?

Both equations are linear (line equations), so we have a linear system of two equations and two unknowns. For Job A, y = 12 x + 100, the slope is 12, and the y-intercept is 100. For Job B, y = 16 x, the slope is 16, and the y-intercept is 0. We can find the point at which both lines intersect:

y = 12 x + 100 ------------>>> 16 x = 12 x + 100 ------------>>> x = 100 / 4 = 25

y(25) = 16 (25) = $ 400

The point of intersection is (25, 400)

Now, you have all information needed to plot both equations.

What job would you decide to take to make the most money and explain your reasoning?

This answer depends on the number of hours worked in a month. If the number of hours worked per month is greater than 25, which is usually the case, then Job B would definitely pay more. You can check that by plugging any value of x greater than 25 in both equations.

I would take Job B!