Question

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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 55 large boxes and
70 small boxes. If the truck is carrying a total of 4850 pounds in boxes, how much does each type of box weigh?

Answer 1

For this case we propose a system of equations:

x: Variable representing the weight of large boxes

y: Variable that represents the weight of the small boxes

So

`x + y = 80\\55x + 70y = 4850`

We clear x from the first equation:

`x = 80-y`

We substitute in the second equation:

`55 (80-y) + 70y = 4850\\4400-55y + 70y = 4850\\15y = 450\\y = 30`

We look for the value of x:

`x = 80-30\\x = 50`

Large boxes weigh 50 pounds and small boxes weigh 30 pounds

Answer:

Large boxes weigh 50 pounds and small boxes weigh 30 pounds

Answer 2

Answer: A large box weighs 50 pounds and a small box weighs 30 pounds.

Explanation:

Set up a system of equations.

Let be "l" the weight of a large box and "s" the weight of a small box.

Then:

`\left \{ {{l+s=80} \atop {55l+70s=4,850}} \right.`

You can use the Elimination method. Multiply the first equation by -55, then add both equations and solve for "s":

`\left \{ {{-55l-55s=-4,400} \atop {55l+70s=4,850}} \right.\\.............................\\15s=450\\\\s=(450)/(15)\\\\s=30`

Substitute
`s=30` into an original equation and solve for "l":

`l+(30)=80\\\\l=80-30\\\\l=50`