I just dont understand this question, could any one tell me how to solve this one?
A pen costs $13$ dollar and a notebook costs $35$ dollar, let $m$ be the maximum number of items that can be bought for $1000$ dollars and $n$ be the minimum number of items that can be bought for the same amount. we need to find $m+n$.
a) 76
b) 88
c) 96
d) 98
Thank you.
The question here is vague so I'll offer a few solutions.
Option 1: You don't have to spend all the money.
Trivial solution for minimum keep all the money and buy nothing $n = 0$
Trivial solution for maximum only buy pens $m = 76$
$m+n = 76$
Option 2: You don't have to spend all the money but must buy if you can afford it.
Buy as many books as you can $28$ you have 20 dollars change so can buy one pen $n=29$
Trivial solution for maximum only buy pens $m = 76$
$m+n = 105$
Option 3: you must spend exactly 1000 dollars
Now we are looking for solutions to $13 \cdot x + 35 \cdot y = 1000$
We know that number of books must be less than 28 and not less than zero we can try them all.
Possible solutions are:
10 books and 50 pens $m = 60$
23 books and 15 pens $n = 38$
$m+n = 98$
Any other numbers of books and you are left with change.
Let $x$ be the number of pens to be bought; let $y$ be the number of notebooks to be bought. Thus, it is implied that $x$ and $y$ are non-negative integers. $m$ is the maximum value of $x+y$ (and $n$ is the minimum value of $x+y$). If we are allowed to spend less than 1000 dollars, then $x$ and $y$ must be chosen so that $13x+35y\le 1000$. If it is required to spend exactly 1000 dollars, then the condition is $13x+35y=1000$.
