I can't figure this out

Question

A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 80

 pounds. The truck is transporting 65

 large boxes and 60

 small boxes. If the truck is carrying a total of 5100

 pounds in boxes, how much does each type of box weigh? 

Answer 1

Hi Sophia,

You can solve this problem by creating a system of 2 equations and solving them using elimination or substitution. Let's try elimination.

First, let's represent the weight of 1 large box with the variable, L, and the weight of 1 small box with the variable, S.

Then we can write the following equations to show the total weight of all boxes and the total weight of 1 large and 1 small box:

L + S = 80

65L + 60S = 5100

Using elimination: Multiply the first equation by -65 to eliminate the variable L first:

-65L + (-65S) = -5200

Now combine this new equation with the remaining original equation to find the value of S:

-65L + (-65S) = -5200

65L + 60S = 5100

-5S = -100

S = 20

The weight of 1 small box is 20 pounds.

Since the total weight of 1 small box and 1 large box is 80 pounds, then 1 large box will weigh 60 pounds.