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I cant solve this word problem:

Courier charges to a certain destination are $65$ cents for first $250$ grams and $10$ cents for each additional $100$ grams or part thereof. What could be the weight of package for which charge is $\$ 1.55$ ?

I am solving it as:

$155 $cents = $65 + 90$ = $250$ grams + $900$ grams (since $10$ cents is for $100$ grams)

I get the answer $1150$ but the answer is suppose to be $1145$.

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We paid an extra $90$ cents. That means that our package weighed more than $250+800$, but its weight was $\le 250+900$. If your question was a multiple choice question, and the only suggested answer in the interval $(1050,1150]$ was $1145$, then $1145$ is the answer to pick. If the question is not multiple choice, all you can say is $\gt 1050$, $\le 1150$. Incredibly cheap courier rates! – André Nicolas Jul 26 '12 at 16:46
Yes the question is multiple choice , sorry i didnt specify that. Could you tell me if my method is wrong ? and how exactly did you get the limit (1050,1050) ? Thanks – MistyD Jul 26 '12 at 16:53
Your method is not really wrong. The $1150$ you got was the maximum possible weight. But the problem says that you pay $10$ cents for every $100$ grams over $250$, or part thereof. That means that if you are $1$ gram more than $250+800$, you get charged just as much as if your package weighs $250+900$. – André Nicolas Jul 26 '12 at 16:59
Thanks I was wondering what the part thereof meant here.. – MistyD Jul 26 '12 at 17:02
@AndréNicolas Could you kindly paste the main response as the answer. So I could end this question – MistyD Jul 26 '12 at 17:03
up vote 0 down vote accepted

We use your analysis. We paid an extra $90$ cents. For that, we could ship a package that weighs $250+ \frac{90}{10}(100)$ grams, that is, $1150$ grams.

But note that the fine print says that we pay $10$ cents for every $100$ grams or part thereof. So if we are "over" the basic $250$ grams, say by $802$ grams, we pay $80$ cents for the $800$ grams, and an extra $10$ cents for the measly $2$ extra grams over $800$. In effect, we are paying as if our package weighed $250+900$. (So we might as well open the package and put a couple of cookies in. The shipping cost won't change.)

Mathematically, all one can say is that if we paid $\$1.55$ to ship the package, then the weight $w$ of the package satisifes the inequality $250+800 \lt w \le 250+900$, that is, $$1050 \lt w \le 1150.$$ If the question was a multiple choice question, and $1145$ was the only "answer" supplied that is in the above interval, then $1145$ is the right answer.

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Suppose you have a package that weights 100 grams. How much does it cost to ship? How about for 200 grams? 300? 400?

Can you describe in words how you calculate the cost if you know the weight. Now let $W$ stand for the weight of the package and $C$ for the cost to ship it. Then turn your description into a mathematical equation.

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I am not really getting the angle – MistyD Jul 26 '12 at 16:25
@MistyD Okay, I added some more suggestions to my answer. Let me know if this helps. – Code-Guru Jul 26 '12 at 16:30

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