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let us consider following problem

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

answer of this problem is $ 1145 $,but i could not understand why,that is what i have tried

so as i understand this question ask that,if for example amount of weight is $850$,then $250$ in this $850$ could be $3$ times ,because $250*3=750$ and we have additional $100$,so total amount of cents would be $3*65+10=215$ right?then how could be $1145$? because $1145/250=4.58$ or $4$ and remainder $0.58$ and $4*65=260$? or $2$ dollar and $60$ cent?please help me

please see this one

and this

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If $x$ is the number of additional $100$ grams $$155=65+10\cdot x\implies x=9$$ Total weight should be $250+100\cdot9=1150$ – lab bhattacharjee Jul 27 '13 at 9:49
but in $1150$ there should be $4*250$ right? – dato datuashvili Jul 27 '13 at 9:50
beyond $250$ grams, we can utilize $10$ cent/$100$ grams which is cheaper than $65$ cents/$250$ grams – lab bhattacharjee Jul 27 '13 at 9:52
but there is question about minimization or what? – dato datuashvili Jul 27 '13 at 9:53
the title says: "maximum amount of weight". – lab bhattacharjee Jul 27 '13 at 9:56
up vote 3 down vote accepted

First, to clarify the question:

It says that if you ordered a package that weighed $250$ grams, it would cost $65$ cents and if it weighed more, then for every additional $100$ grams or part thereof, it would cost $10$ cents extra. The "part thereof" means that even if the additional weight isn't exactly a whole multiple of $100$ grams, the cost would be $10$ cents for each $100$ grams and another $10$ cents for the remainder. So for example:

If the weight of the package you ordered was $250$ grams, then the cost would be $65$ cents. If it was $350$ grams, then the cost would be $75$ cents ($10$ cents extra for each additional $100$ grams). Now what if its weight was $400$ grams? The additional weight is $400-250=150$ grams. The $100$ grams of this weight would cost you $10$ cents and the remaining $50$ grams would cost you another $10$ cents. This is what the "part thereof" of your question means. So the cost would be $65+10+10=85$ cents. Similarly, if the weight was $450$, it would still cost $85$ cents, and if the weight was $451$ grams, it would cost $95$ cents.

Since the final charge is $155$ cents which is greater than $65$ cents, the weight must be greater than $250$ grams. The cost of the additional weight is then $155 -65=90$ cents. Now the $80$ cents out of these $90$ cents was for an additional weight of $80*\frac{100}{10} = 800$ grams. Thus the weight must be more than $800+250=1050$ grams. If we add another $100$ grams, the additional cost would then become $90$ cents, but note that it would become $90$ even if we it weighed an additional $1$ gram instead of the $100$ grams. Thus the weight of the package must be greater than $1050$ grams and less than or equal to $1150$ grams. Since $1145$ lies within this range, the answer is $1145$ grams.

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ok i understood,only question what i had,why it could be for example calculate weight in terms of $250$,thanks very much – dato datuashvili Jul 27 '13 at 10:14
@dato Are you asking why the approach you took in solving the problem is incorrect? – Alraxite Jul 27 '13 at 10:19
i would post question and answer – dato datuashvili Jul 27 '13 at 10:22
@dato Oh, I think the question isn't exactly what I thought. I'll edit my answer to incorporate this. – Alraxite Jul 27 '13 at 10:29
@dato Please read my answer. I've edited it. – Alraxite Jul 27 '13 at 11:09

The total amount given here is $1.55.Let us first convert it to cents,i.e.,155 cents.Now it exceeds the fixed charge by 155-65 = 90 cents.Till this point we have total weight as 250 grams corresponding to the fixed charge we deducted.Now additional 10 cents are charged for every 100 grams.This leads to the equation (90/10) x 100 for getting the extra grams of weight.That gives us the amount 900 grams.So now the total weight of the package will be 250 + 900 = 1150 grams.But the amount here will be the maximum possible weight for which the amount will be 155 cents.For the minimum possible weight we need to consider 801 grams of weight as 800 grams of weight will lead to the total amount to be 145 cents.Thus the minimum possible weight is 1051 grams.So you will get your answer anything between 1051-1150 grams.

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