Jack works after school. Each day he is paid a set amount, plus an hourly wage. Look at the table.

Question

Hours	1	1.5	2	2.5	3
Pay	22	28	34	40	46

Assume Jack works from 2:30 P.M. to 8:00 P.M. How much does he earn?



A.$40

B.$62.50

C.$65

D.$76

Answer 1

Hi Anastasia,

First we need to figure out how many hours Jack worked. He worked from 2:30 PM to 8:00 PM, so that's 5.5 hours. (8 - 2.5 = 5.5)

Now we need to figure out the formula for how he gets paid. We know it's a set amount plus an hourly wage, so let's figure out those numbers from the table.

The pay formula must be:

P = S + W*h

where,

P=payment

S=set amount he makes

W=Jack's wage

h=# of hours Jack worked

I know this must be the formula naturally based on the question, his payments are made up of a set amount plus an hourly wage, and the hourly wage would be the # of hours worked multiplied by his wage.

Let's use known information from the table to figure out W and S.

If he works 1 hour, he gets $22.

P = S + W*h

22 = S + W*(1)

So, we know that S + W = 22

If he works 2 hours, he gets $34.

P = S + W*h

34 = S + W*(2)

So, we know that S + 2*W = 34

Now I have 2 variables & 2 equations. Anytime this is the case, we can solve for both variables now!

S + W = 22

S + 2*W = 34

Let's solve for S in first equation and substitute into second equation.

S = (22-W)

Therefore,

(22-W) + 2*W = 34

22 - W + 2W = 34

W = 34 - 22

W = 12

Now plug 12 in for W in the first equation to solve for S.

S + W = 22

S + 12 = 22

S = 10

Now we know Jack's wage is $12/hour and his set amount is $10.

P = S + W*h

P = 10 + 12*h

The question asks how much he earns working 5.5 hours. Let's plug it in the equation.

P = 10 + 12*h

P = 10 + 12*(5.5)

P = 10 + 66

P = 76

So the answer is $76.

Hope this helps. :)