Question

PLZ HELP A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 55 pounds each, and the small boxes weigh 35 pounds each. There are 125 boxes in all. If the truck is carrying a total of 4950 pounds in boxes, how many of each type of box is it carrying?

Answer 1

There were 28.75 large boxes and 96.25 small boxes.

Explanation:

Create a system of equations to solve.

State your variables

let x be the number of small boxes

let y be the number of large boxes

35x + 55y = 4950 Equation for weight

x + y = 125 Equation for number of boxes

Rearrange equation for number of boxes to isolate "x".

x = 125 - y

Substitute the new equation into the equation for weight

35x + 55y = 4950

35(125 - y) + 55y = 4950

Expand the brackets

4375 - 35y + 55y = 4950 Combine like terms

4375 + 20y = 4950

Start isolating "y"

4375 + 20y = 4950

4375 - 4375 + 20y = 4950 - 4375 subtract 4375 from both sides

20y = 575

20y/20 = 575/20 divide both sides by 20

y = 28.75 number of large boxes

Calculate "x". Rearrange the equation for number of boxes to isolate "y".

y = 125 - x Substitute this expression

35x + 55y = 4950 equation for weight

35x + 55(125 - x) = 4950 expand the brackets

35x + 6875 - 55x = 4950 combine like terms

6875 - 20x = 4950 start isolating "x"

6875 - 6875 - 20x = 4950 - 6875 subtract 6875 on both sides

-20x = -1925

-20x/-20 = -1925/-20 divide both sides by -20

x = 96.25 number of small boxes

There is a mistake with this question because you should not be able to have partial boxes. However, the answer is:

There were 28.75 large boxes and 96.25 small boxes.