149k views
4 votes
A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 70 pounds. The truck is transporting

50 large boxes and 70 small boxes. If the truck is carrying a total of 4100 pounds in boxes, how much does each type of box weigh?

User Nomi
by
8.8k points

1 Answer

2 votes

Answers:

one small box = 30 pounds

one large box = 40 pounds

==========================================================

Work Shown:

  • S = weight of one small box
  • L = weight of one large box

S+L = 70 since the two boxes combine to 70 pounds.

70S = weight of 70 small boxes

50L = weight of 50 large boxes

70S+50L = weight of 70 small and 50 large

70S+50L = 4100

The system of equations is


\begin{cases}S+L = 70\\70S+50L = 4100\end{cases}

There are a few ways to solve this system. I'll use substitution.

I'm going to isolate L in the first equation like so

S+L = 70

L = 70-S

Which I'll then plug into the other equation to solve for S

70S+50L = 4100

70S+50(70-S) = 4100

70S+3500-50S = 4100

20S+3500 = 4100

20S = 4100-3500

20S = 600

S = 600/20

S = 30

Each small box is 30 pounds.

Use this value of S to find L

L = 70-S

L = 70-30

L = 40

Each large box is 40 pounds.

Like we expect, each large box weighs more compared to any given small box.

------------------

Check:

  • S+L = 30+40 = 70 verifies the first equation
  • 70S+50L = 70*30+50*40 = 4100 verifies the second equation

Both equations are true for the ordered pair (S,L) = (30,40). Therefore, the answers have been confirmed.

User Anders Arpi
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.