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

Thank you for the opportunity to help you with your question!

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.


Please let me know if you need any clarification. I'm always happy to answer your questions.
Nov 15th, 2015

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