Large boxes: L, 45 lb
Small boxes: S, 30 lb
There are 125 boxes, then:
[tex]L+S=125[/tex]
The total weight in boxes is 4575 lb:
[tex]\begin{gathered} 45L+30S=4575 \\ \Rightarrow\frac{45L}{15}+\frac{30S}{15}=\frac{4575}{15} \\ \Rightarrow3L+2S=305 \end{gathered}[/tex]
Then, the system of equations is:
[tex]\begin{cases}L+S=125\ldots(1) \\ 3L+2S=305\ldots(2)\end{cases}[/tex]
From (1), L = 125 - S, so we use this on (2):
[tex]\begin{gathered} 3(125-S)+2S=305 \\ 375-3S+2S=305 \\ S=70 \end{gathered}[/tex]
Using this result on (1):
[tex]\begin{gathered} L+70=125 \\ \Rightarrow L=55 \end{gathered}[/tex]
There are 55 large boxes and 70 small boxes
