Question 235464
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Since you said *[tex \LARGE A\ +\ B\ =\ 2388.9], you must mean that *[tex \LARGE A] represents the amount of A's paycheck and *[tex \LARGE B] represents the amount of B's paycheck.  That is certainly a reasonable start.


But if *[tex \LARGE A] represents A's paycheck, then *[tex \LARGE \frac{A}{2}] must represent what A earns in 1 hour, or the hourly rate for A.  Likewise, *[tex \LARGE \frac{B}{43}] 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, *[tex \LARGE s].


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{A}{2}\ +\ \frac{B}{43}\ =\ s]


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 *[tex \Large a] represent the hourly rate earned by A, and *[tex \Large b] represent B's hourly rate.  That way I could say that *[tex \Large 2a] was the amount of A's paycheck and *[tex \Large 43b] was the amount of B's paycheck, and finally, the sum is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2a\ +\ 43b\ =\ 2388.9]


But then I am also stuck for any other information that gives me a different relationship between *[tex \Large a] and *[tex \Large b].


The only thing that you can do is to graph the linear relationship and find the intercepts so that you can say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 0\ \leq\ a\ \leq\ 1194.45]


and then once *[tex \Large a] is chosen, *[tex \Large b] can be calculated but will be in the range:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 0\ \leq\ b\ <\ 55.56]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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