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Mathematics 40 Online
OpenStudy (blenchiki):

Grace can purchase a research report from the library for $15.00, or she can borrow the report and produce a copy at a cost of $0.06 per page. If the cost to purchase the report is exactly equal to the cost to reproduce it, then the report must have how many pages?

OpenStudy (mathstudent55):

You don't know the number of pages, so the number of pages in an unknown. In algebra, we let a variable, usually a letter, represent an unknown. Let x = number of pages. Ok so far?

OpenStudy (blenchiki):

okay

OpenStudy (mathstudent55):

On page costs $0.06. The report will have x pages. How much do x pages cost?

OpenStudy (mathstudent55):

We don't know what the cost is since we don't know what x is, but using x, and using the price per page of $0.06, what expression gives you the cost of x pages?

OpenStudy (blenchiki):

$0.06x=x?

OpenStudy (blenchiki):

becauase you would multiply the amount of papers with how much they cost in order to get the total?

OpenStudy (mathstudent55):

You're on the right track. The cost of x pages at $0.06 per page is simply 0.06x If you multiply the number of pages, x, by the cost per page, you get 0.06x, which is the cost of all the pages.

OpenStudy (mathstudent55):

Correct. Just don't set it equal to x since x is just the number of pages.

OpenStudy (blenchiki):

okay thank you!

OpenStudy (mathstudent55):

You're doing great so far. Now we know that with x pages, the paper will cost 0.06x

OpenStudy (blenchiki):

is that the answer or more to it? how do we find x?

OpenStudy (mathstudent55):

The question is how many pages. The answer must be a number. We're not done yet, but we're close.

OpenStudy (blenchiki):

okay

OpenStudy (mathstudent55):

Now they tell us "If the cost to purchase the report is exactly equal to the cost to reproduce it, then the report must have how many pages?" We can write the above as an equation: \(\large \color{red}{cost~ to ~purchase ~the ~report} = \color{blue}{cost ~to ~reproduce ~it}\) \(\large \color{red}{The ~cost ~to ~purchase ~it ~= $15}\) \(\large \color{blue}{The ~cost ~to ~reproduce ~it =~ the ~cost ~of ~the ~copies = 0.06x}\) We now get the equation \(\large 15 = 0.06x\) Now we need to solve the equation for x.

OpenStudy (blenchiki):

so we divide both sides by 15 and x= 250?

OpenStudy (mathstudent55):

We can switch sides to get \(\large 0.06x = 15\) We want x alone. x in being multiplied by 0.06, so we divide both sides by 0.06. \(\large \dfrac{\cancel{0.06}x}{\cancel{0.06}} = \dfrac{15}{0.06} \) \(\large x = 250\)

OpenStudy (mathstudent55):

You are correct.

OpenStudy (mathstudent55):

Your answer is correct, but we divided both sides by 0.06, not 15.

OpenStudy (blenchiki):

thank you for explaining it to me

OpenStudy (mathstudent55):

The answer is: the report has 250 pages. You can just write: 250 pages. The answer is not: x = 250 We used an equation with x to solve the problem and arrive at an answer. The person asking the question has no idea what x is. We must answer the question with a response that makes sense to0 the person who asked the question.

OpenStudy (mathstudent55):

You're welcome.

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