SOLUTION: A typist figures out that if she types 2 pages above her work quota daily, she will complete her work 3 days ahead of schedule, and if she makes 4 pages extra per day, she will fin

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Question 1094822: A typist figures out that if she types 2 pages above her work quota daily, she will complete her work 3 days ahead of schedule, and if she makes 4 pages extra per day, she will finish 5 days ahead of time. How many pages does she have to type and in how many days?
Please show full solution, and solve algebraically.
Thank you!

Answer by ikleyn(52833) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let P = the number of pages to print daily according to the schedule, and let D = the number of days to print according to the schedule.

Then you have these two equations

(P+2)*(D-3) = P*D    (1)   (P*D = total number of pages) 
(P+4)*(D-5) = P*D    (2)    

We have two equations in two unknowns, but the equations are non-linear.
Simplify each of the equations. Equation (1) becomes 

PD + 2D - 3P - 6 = PD,  or,  canceling PD in both sides,
2D - 3P - 6 = 0,  or
2D - 3P = 6.         (3)


Equation (2) becomes 

PD + 4D - 5P - 20 = PD,  or,  canceling PD in both sides,
4D - 5P - 20 = 0,  or
4D - 5P = 20.        (4)


Now we have an equivalent system of two equations (3) and (4) in two unknowns, but this time the equations are linear:

2D - 3P = 6.         (3)
4D - 5P = 20.        (4)


Multiply equation (3) by 2 and then subtract from equation (4) (both sides). You will get

-5P - (-6P) = 20 -12 = 8  --->  P = 8. 

Thus the number of pages to be printed daily is 8, according to the schedule.

Then from (3) 2D = 6 + 3*P = 6 + 3*8 = 30  ====>  D = 15.


Answer. The schedule is to print 8 pages daily in 15 days.

Check the answer on your own.


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    - Had they sold . . .
in this site.


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Miscellaneous word problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
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to your archive and use it when it is needed.