How can I equal the Sum two different Quantity with different prices

Question

Example I'm gonna buy two box of Books. $1$ Box each store
The $1$st Box has Price of 250 per book with $80$ pcs of Books.
The $2$nd Box has Price of 280 per book with $65$ pcs of Books.

So the price of $1$st box is $250 \times 80 = 20,000$
and the price of $2$nd box is $280 \times 65 = 18,200 $
So the Total Price of two box is $38,200$

Is there a way If I Sum both Price and Quantity which is
$250 + 280 = 530$
$80 + 65 = 145$

Is there a mathematical way to solve these two values $(530$ & $145)$ and still get "$38,200$" in Total

It's not reasonable to do that. Why are you adding prices to each other and likewise adding quantities? — Leyla Alkan, Mar 21 '18 at 06:38
I'm not sure if its possible but its a way to solve my problem in programming. rolf — user3410460, Mar 21 '18 at 06:39
Something like this $(250+280)(80+65)-250\cdot 65-280\cdot 80=38200$ ? — Leyla Alkan, Mar 21 '18 at 06:47

score 0 · Accepted Answer · answered Mar 21 '18 at 06:48

No, this is not possible: the total price is not determined by those two sums. To be more precise, if you have four numbers $a,b,c,$ and $d$, then $ac+bd$ cannot be uniquely determined from $a+b$ and $c+d$ (here $a$ and $b$ are the two prices and $c$ and $d$ are the respective quantities).

For example, consider $a=b=c=d=2$ and $a'=c'=1$, $b'=d'=3$. Then $a+b=a'+b'=4$ and $c+d=c'+d'=4$. However, $ab+cd=8$ is not the same as $a'b'+c'd'=6$.

How can I equal the Sum two different Quantity with different prices

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