Question

Please help See attached photoWorking with system of linear problems not a quiz or homework knowledge check and at the bottom gives you explanation

Answer 1

Large boxes: L, 45 lb

Small boxes: S, 30 lb

There are 125 boxes, then:

`L+S=125`

The total weight in boxes is 4575 lb:

`\begin{gathered} 45L+30S=4575 \\ \Rightarrow(45L)/(15)+(30S)/(15)=(4575)/(15) \\ \Rightarrow3L+2S=305 \end{gathered}`

Then, the system of equations is:

`\begin{cases}L+S=125\ldots(1) \\ 3L+2S=305\ldots(2)\end{cases}`

From (1), L = 125 - S, so we use this on (2):

`\begin{gathered} 3(125-S)+2S=305 \\ 375-3S+2S=305 \\ S=70 \end{gathered}`

Using this result on (1):

`\begin{gathered} L+70=125 \\ \Rightarrow L=55 \end{gathered}`

There are 55 large boxes and 70 small boxes