Question 235464: Employee A and Employee B paychecks totaled $2,388.90. Employee A worked two hours and Employee B worked 43 hours during this time period. What is each of their hourly rate? (There hourly rates may (probably will) be different.)
A + B = $2,388.90
A/2 + B/43 = $2,388.90
This is what I think the two problems are supposed to be, but when I solve one for A to substitute in the other, it isn't working. HELP!!
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Since you said  , you must mean that  represents the amount of A's paycheck and  represents the amount of B's paycheck. That is certainly a reasonable start.
But if represents A's paycheck, then  must represent what A earns in 1 hour, or the hourly rate for A. Likewise,  must be the hourly rate for B. Certainly what each of them make in 1 hour cannot add up to the same amount that they both earn in a total of 45 hours. Hence your second equation is faulty because you don't know the constant amount, that is you have actually introduced a third variable, call it the sum of the rates,  .
Now what do we do? Not much, I'm afraid. Without additional information, you are stuck.
I started the problem from a different direction. I let  represent the hourly rate earned by A, and  represent B's hourly rate. That way I could say that  was the amount of A's paycheck and  was the amount of B's paycheck, and finally, the sum is:
But then I am also stuck for any other information that gives me a different relationship between and .
The only thing that you can do is to graph the linear relationship and find the intercepts so that you can say:
and then once is chosen, can be calculated but will be in the range:
John
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