SOLUTION: Hi Peter was given a box of pens. He sold all the pens. Each pen was sold at $8.90. For every set of 5 pens sold a pen was given free. 2/3 of the pens were sold in sets of 5 pe

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Question 1168690: Hi
Peter was given a box of pens. He sold all the pens. Each pen was sold at $8.90. For every set of 5 pens sold a pen was given free. 2/3 of the pens were sold in sets of 5 pens. He collected $1174.80 how many pens were in the box at first.
Thanks


Found 3 solutions by greenestamps, Theo, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


I think you need to re-post the problem, making it more clear. As you have posted it here, I don't see any way to interpret it to get a reasonable answer.

For one thing, it is not clear whether $8.90 is the average selling price of all the pens, or if it is the average selling price of only the pens that were not given away free.

My interpretation is that 1/3 of the pens were sold at $8.90 each and 2/3 of them were sold at 5/6 of $8.90 each, because those 2/3 of the pens were sold at 6 for the price of 5. Using x for the total number of pens, that gives us

%281%2F3%29%28x%29%288.90%29%2B%282%2F3%29%285%2F6%29%28x%29%288.90%29+=+1174.80
%288%2F9%29%28x%29%288.90%29+=+1174.80
%288%2F9%29x+=+1174.80%2F8.90+=+132
x+=+132%2F%288%2F9%29+=+132%2A%289%2F8%29+=+148.5

That doesn't make sense; the original number of pens has to be a whole number.

I will be curious to see if another tutor comes up with an interpretation of the problem that leads to a reasonable answer.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
x = number of pens sold separately.
y = number of pens sold in sets of 5.
when the pens are sold separately, they cost 8.90 each.
when the pens are sold in sets of 5, they cost 44.50 plus the buyer gets a pen for free.
your cost equation is 8.90 * x + 44.50 * y = 1174.80.
8.90 is the cost for one pen sold separately.
44.50 is the cost of a set of 5 pens with 1 extra pen given for free.
you are given that 2/3 of the pens were sold in sets of 5.
since (x + y) is the total number of pens sold, this means that y = 2/3 * (x + y)
simplify to get y = 2/3 * x + 2/3 * y
subtract 2/3 * y from both sides of this equation to get:
y - 2/3 * y = 2/3 * x
combine like terms to get:
1/3 * y = 2/3 * x
solve for y to get:
y = 3/1 * 2/3 * x
simplify to get:
y = 2 * x
in the equation of 8.90 * x + 44.50 * y = 1174.80, replace y with 2 * x to get:
8.90 * x + 44.50 * 2 * x = 1174.80.
simplify to get:
8.90 * x + 89 * x = 1174.80
combine like terms to get:
97.90 * x = 1174.80
solve for x to get:
x = 12.
since y = 2 * x, then you get:
y = 24.
your equation of 8.90 * x + 44.50 * y = 1174.80 becomes:
8.90 * 12 + 44.50 * 24 = 1174.80 which becomes 1174.80 = 1174.80, confirming the values of x and y are good.
x represents 1 pen.
y represents 6 pens (5 that are bought and 1 that is given free).
12 * 1 + 24 * 6 = 156.
there must have been 156 pens in the box.
that's your solution, as best i can determine.
he sold 12 pens separately.
he sold 24 sets of 5 pens each = 120 pens
he gave away 24 pens (1 for each set of 5).
the total pens in the box had to be 12 + 120 + 24 = 156.
132 of the pens were sold.
24 were given away.

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

As the problem is worded, printed, posted and presented, it is only good to frighten students.

Good only for re-cycling.

It is not the tutors duty to edit or interpret such gibberish.

In opposite, it is the student/visitor duty to provide a correct input.



At this forum, several tutors try to perform a role of a "kind policemen" and interpret nonsensical posts,
even without editing them and without pointing to the authors why their posts make no sense.


I, however, think that more honest way (and much more educational) is to call nonsense as a nonsense.



Many times, when I see not perfectly formulated posts at the forum, I edit them, when I see some sense in it.


But, clearly, not in this case, when so called "composer" does not know himself what he wants to present.