Question 1195578
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A delivery truck is transporting boxes of two sizes: large and small. 
The combined weight of a large box and a small box is 65 pounds. 
The truck is transporting 55 large boxes and 65 small boxes. 
If the truck is carrying a total of 3775 pounds in boxes, 
how much does each type of box weigh?
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            This problem can be solved in two ways.


            One way is to use two unknowns and a system of two equation.

            Another way is to use SINGLE unknown and one equation.

            Since the second way is simpler/shorter,  I choose it to solve the problem.



<pre>
Let x be the weight of the smaller box, in pounds.

then the weight of the larger box is (65-x) pounds, according to the problem.


Now, I write equation for the total weight

     65x + 55*(65-x) = 3775  pounds.


Simplify and find x

    65x + 55*65 - 55x = 3775

    65x - 55x         = 3775 - 55*65

        10x           =     200

          x           =     200/10 = 20.


<U>ANSWER</U>.  Small boxes weight 20 pounds each.

         Large boxes weight  65-20 = 45 pounds each.


<U>CHECK</U>.  Total weight is  65*20 + 55*45 = 3775 pounds,    correct !
</pre>

Solved.