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 85 pounds. The truck is transporting 55 large boxes and 60 small boxes. If the truck is carrying a total of 4850 pounds in boxes, how much does each type of box weigh?Large box: Small box: Solve by using system of linear equations.

Answer 1

Given:

Two boxes - large and small

`\begin{gathered} Let\text{ the large boxes be represented by }l \\ Let\text{ the small boxes be represented by }s \end{gathered}`

Generate the system of equations from the statements given:

`\begin{gathered} Total\text{ w}eight\text{ of each box is 85 pounds} \\ l+s=85 \\ \\ Total\text{ weight of truck is 4850 pounds} \\ 55l+60s=4850 \end{gathered}`

Solving both equations simultaneously;

`\begin{gathered} l+s=85...................................(1) \\ 55l+60s=4850.........................(2) \\ \\ From\text{ equation \lparen1\rparen,} \\ s=85-l.............................(3) \\ \\ Substitute\text{ s into equation \lparen2\rparen;} \\ 55l+60(85-l)=4850 \\ 55l+5100-60l=4850 \\ 55l-60l=4850-5100 \\ -5l=-250 \\ Divide\text{ both sides by -5} \\ l=(-250)/(-5) \\ l=50 \end{gathered}`

Substitute l into equation (3) to get s

`\begin{gathered} s=85-l \\ s=85-50 \\ s=35 \end{gathered}`

Therefore,

Large box: 50 pounds

Small box: 35 pounds