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Question 1203933: A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 40 pounds each, and the small boxes weigh 25 pounds each. There are 120 boxes in all. If the truck is carrying a total of 3750 pounds in boxes, how many of each type of box is it carrying?
Found 4 solutions by math_tutor2020, AngelSchuck, josgarithmetic, Edwin McCravy:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
x = number of large boxes
120-x = number of small boxes
40x = weight of the large boxes only
25(120-x) = weight of the small boxes only
40x + 25(120-x) = total weight = 3750
40x + 25(120-x) = 3750
Let's solve for x.
40x + 25(120-x) = 3750
40x + 3000-25x = 3750
15x + 3000 = 3750
15x = 3750-3000
15x = 750
x = 750/15
x = 50
120-x = 120-50 = 70
Answers:
50 large boxes and 70 small boxes
Answer by AngelSchuck(1) (Show Source):
You can put this solution on YOUR website! x = number of large boxes
120-x = number of small boxes
40x = weight of the large boxes only
25(120-x) = weight of the small boxes only
40x + 25(120-x) = total weight = 3750
40x + 25(120-x) = 3750
Let's solve for x.
40x + 25(120-x) = 3750
40x + 3000-25x = 3750
15x + 3000 = 3750
15x = 3750-3000
15x = 750
x = 750/15
x = 50
120-x = 120-50 = 70
Answers:
50 large boxes and 70 small boxes
Answer by josgarithmetic(39618) (Show Source):
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website! A delivery truck is transporting boxes of two sizes: large and small. The large
boxes weigh 40 pounds each, and the small boxes weigh 25 pounds each. There are
120 boxes in all. If the truck is carrying a total of 3750 pounds in boxes, how
many of each type of box is it carrying?
For interesting enrichment in your mathematical thinking about this problem,
let's look at the "no-algebra" way to do it -- the only way you could have done
it when you were in elementary school! Some elementary school teachers have
labeled it the "WHAT IF?" method.
If all 120 boxes had weighed only 25 pounds each, the truck
would be carrying only (120)(25) = 3000 pounds. So some of
the 120 boxes must each weigh 40-25 = 15 pounds heavier to
cause the cargo to weigh 3750-3000 = 750 pounds heavier. So
there must be 750/15 = 50 large boxes, and 120-50 = 70 small
boxes.
Or you could go this route instead without using algebra:
If all 120 boxes had weighed 40 pounds each, the truck would
be carrying (120)(40) = 4800 pounds. So some of the 120
boxes must each weigh 40-25 = 15 pounds lighter to cause the
cargo to weigh 4800-3750 = 1050 pounds lighter. So there
must be 1050/15 = 70 small boxes, and 120-70 = 50 large boxes.
Edwin
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