Question 1195578: 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?
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
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.
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.
ANSWER. Small boxes weight 20 pounds each.
Large boxes weight 65-20 = 45 pounds each.
CHECK. Total weight is 65*20 + 55*45 = 3775 pounds, correct !
Solved.
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