word problem help

Question

An online fax company, EFaxIt.com, has a customer plan where a subscriber pays a monthly subscription fee of $16.75 dollars and can send/receive 100 fax pages at no additional cost. For each page sent or received past the 100 page limit, the customer must pay an overage fee of $0.05 per page. The following expression gives the total cost, in dollars, to send  pages beyond the plan's monthly limit.

C= $0.05p+$16.75

If the monthly bill under this plan comes out to be $18.3, what was the total number of pages that were sent or received?



Answer 1

So this just seems complicated because they threw a lot of words at you. Let's look at the facts we were given:

1) The subscription plan costs $16.75

2) The subscription plan includes 100 pages

3) The monthly bill under this plan came out to be $18.30

4) Each extra page costs $0.05

They were nice enough to give us an equation, but if it's more intuitive NOT to use it, I'll solve that way first (even though we really are using it without knowing).

so we have a total cost of $18.30 -- let's subtract the subscription cost of $16.75 (don't forget that this includes 100 pages!)

18.30

-16.75

$1.55

Cool -- an extra $1.55, and we know that each additional page costs $0.05, so let's divide $1.55/$0.05.

It comes to 31 if we plug it into our calculator, but, if you're not allowed a calculator, there's an easy way to solve: get rid of the decimals. They're in the same place (to the hundredths), so 155/5 is the same as 1.55/0.05. Then you can long divide!

That means our answer is 131.

Now let's use that nice equation they gave us.

C (cost) = $0.05p(number of pages) + $16.75

Our cost was $18.30

18.30 = 0.05p + 16.75

-16.75 - 16.75

1.55 = 0.05p

1.55/0.05 =0.05p/0.05

31 = p

(+100 for the subscription)

131 pages

I know this is more than half a year later, but I hope this helps in the future!