SOLUTION: The math department bought some calculators for a total of $240 . The department head kept one for the math office and then sold the rest for 300 making a profit of $ 5 on each cal

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Question 1154401: The math department bought some calculators for a total of $240 . The department head kept one for the math office and then sold the rest for 300 making a profit of $ 5 on each calculator . How many calculators did the math department buy ?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
The math department bought some calculators for a highlight%28cross%28lot%29%29 total of $240 .
The department head kept one for the math office and then sold the rest for $300 making a profit of $5
on each calculator. How many calculators did the math department buy ?
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Let n be the number of calculators the department bought.


Then it sold (n-1) calculator.


The buying price for each single calculator was 240%2Fn.

The selling price was  300%2F%28n-1%29.

The difference in prices was 5 dollars


    300%2F%28n-1%29 - 240%2Fn  = 5   dollars.


Simplify dividing by 5 both sides


    60%2F%28n-1%29 - 48%2Fn = 1


Multiply both sides by n*(n-1)


    60n - 48*(n-1) = n*(n-1)

    60n - 48n - 48 = n^2 - n

    n^2 - 13n - 48 = 0

    (n-16)*(n+3) = 0


Of two roots, 16 and -3, only positive n= 16 is meaningful.


ANSWER.  16 calculators were bought.


Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Tutor @ikleyn has provided a perfectly good algebraic solution; here is a very different approach....

The math department bought n calculators for d dollars each, for a cost of $240:

nd+=+240

They sold (n-1) calculators for (d+5) dollars each, for a total of $300:

%28n-1%29%28d%2B5%29+=+300
nd-d%2B5n-5+=+300
240-d%2B5n-5+=+300
d+=+5n-65
n%285n-65%29+=+240
n%28n-13%29+=+48
n%5E2-13n-48+=+0
%28n-16%29%28n%2B3%29+=+0
n+=+16 or n+=+-3

Obviously the negative answer makes no sense. So the number of calculators the math department bought was 16.

CHECK:
16 calculators for $240 means $15 each.
16-1 = 15 calculators for $15+$5 = $20 each makes $300.