Use the table to determine an equation

Question

The table below represents the number of hours a student worked and the amount of money that student earned. Write an equation that represents a number of dollars earned, d, earned in the terms of hours worked, h.

h d

4 $48

10 $120

12 $144

15 $180

Use the equation you wrote to determine the number of dollars the student would earn for working 35 hours.

Answer 1

Hi Arionna,

So this is a two-step problem meaning we have two tasks we need to accomplish in order to find our answer. First--> we have to come up with an equation that shows how many dollars were earned (d) in terms of hours worked.

Second --> we have to use this equation to determine how much money the student earned for working 35 hours

To solve the first half of the problem (making our equation), our goal is to figure out how many dollars the student earns (d) for every hour (h) worked--so we need to use the numbers provided to find out how many dollars the student earns PER every 1 hour worked. Once we know how much money the student earns for working 1 hour, we can figure out how much money the student makes for any number of hours.

So to find out how much money the tutor makes for 1 hour of work, we would use a proportion:

dollars

hour

This can also be read as dollars PER hour. Picking any of the given data points from the table, we can plug those figures into the proportion to discover how many dollars the tutor makes per hour. The simplest math would be using the data point which tells us that the student worked 10 hours and earned $120. Plugging these numbers into our proportion would read:

$120

10 hrs

From here it is basic division: $120/10 = $12 earned per every 1 hour worked. We can double check this by using a second data set from the table: $144 earned for 12 hours worked. Plugging it into our proportion would show $144 over 12 and when divide (144/12) we get $12 earned per every 1 hour worked again.

Now that we know that the student makes $12 per hour, we can make our equation:

d (representing dollars earned) = $12h ($12 representing the constant pay rate-$12/hr; and h representing the changing number of hours worked)

So our equation is d = $12h

NOW we can move on to the second (and easier) half of the problem. Now that we have our equation we can simply plug in the given number of hours worked which is 35. Therefore, our equation will read -->

d = $12(35)

d = $420

Our equation tells us that the student would earn $420 after working for 35 hours, thus finishing the problem. If we want or need to, we can double check our answer using division: 420 / 12 = 35 or 420 / 35 = $12 to ensure we have the correct answer.

Answer 2

This is a linear function. Use two points to find the slope m (4,48) (10,120). find change in y over change in x.

120-40

_________ = m 12=m use y=mx+b and point (4,48) x=4,y=48, m=12

10-4 48=12(4) + b

48=48+b

48-48=b

72 0=b

----- = m y=12x , in terms of d and h D(h)=12h

6 for 35 hours D(35)= 12(35)

Answer 3

48 / 4 = 12

120 / 10 = 12

144 / 12 = 12

180 / 12 = 12

d / h = 12

Therefore, the equation that represent the number of dollars earned in terms of the hours worked is:

d = 12 • h

If the student worked 35 hours:

d = 12 • 35

d = 420

If the student worked 35 hours, he/she will earn $420.

Answer 4

If you divide d by h you will get 12 each time

So d/h = 12, so d = 12h (gets paid $ 12 per hour)

So then put h=35