##### Need algebra help for solving a value mixture problem using a system of linear equations

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A delivery truck is transporting boxes of two sizes: large and small.  The large boxes weigh 50lbs each, and the small boxes weigh 35lbs each. There are 120 boxes in all.  If the truck is carrying a total of 5025lbs in boxes, how many of each type of box is it carrying?

Nov 15th, 2015

We need to assign variables to what we do not know.

Let x = the number of large boxes weighing 50 lbs.each.

Let y = the number of small boxes weighing 35 lbs each.

If there are 120 boxes in all, that means that x + y = 120, right?

Also notice the relationship:  (# of pounds of large boxes) = (50 pounds per box)* x

and  (# of pounds of small boxes) = (35 pounds per box)* y

so   50x + 35y = 5025

Our system of equations is

x + y = 120

50x + 35y = 5025

We can solve by substitution.

y = 120 - x

50x + 35*(120 - x) = 5025

50x + 4200 - 35x = 5025

15x + 4200 = 5025

15x = 825

x = 825/15 = 55  large boxes

y = 120 - x = 120 - 55 = 65 small boxes.

Therefore there are 55 large boxes and 65 small boxes.

Nov 15th, 2015

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Nov 15th, 2015
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Nov 15th, 2015
Oct 24th, 2017
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