Solution:
Let the number of large boxes be
[tex]=x[/tex]
Let the number of small boxes be
[tex]=y[/tex]
The total number of boxes are
[tex]=115[/tex]
The system of equation to represent this will be given below as
[tex]x+y=115\ldots\ldots(1)[/tex]
The large box weigh
[tex]55\text{ pounds each}[/tex]
The small box weigh
[tex]20\text{ pounds each}[/tex]
The total weight of the boxes is
[tex]=4575\text{ pounds}[/tex]
The system of the equation to represent this is
[tex]55x+20y=4575\ldots\text{.}(2)[/tex]
Step 1:
From equation (1) make x the subject of the formula to form equation (3)
[tex]\begin{gathered} x+y=115 \\ x=115-y\ldots\ldots(3) \end{gathered}[/tex]
Step 2:
substitute equation (3) in equation (2)
[tex]\begin{gathered} 55x+20y=4575 \\ x=115-y \\ 55(115-y)+20y=4575 \\ 6325-55y+20y=4575 \\ -35y=4575-6325 \\ -35y=-1750 \\ \text{divide both sides by -35} \\ \frac{-35y}{-35}=\frac{-1750}{-35} \\ y=50 \end{gathered}[/tex]
Substitute the value of y=50 in equation (3)
[tex]\begin{gathered} x=115-y \\ x=115-50 \\ x=65 \end{gathered}[/tex]
Hence,
Number of large boxes = 65
Number of small boxes = 50
