Answer:
Number of large boxes: 55
Number of small boxes: 70
Explanation:
Let x represent the number of the large boxes
Let y represent the number of the small boxes
From the given information in the question, we can go ahead and set up the below system of equations;
[tex]\begin{gathered} 45x+30y=4575\ldots\ldots\ldots\text{Equation 1} \\ x+y=125\ldots\ldots.\ldots.\ldots\text{Equation 2} \end{gathered}[/tex]
We'll follow the below steps to solve the above system of equations simultaneously;
Step 1: Express y in terms of x in Equation 2;
[tex]y=125-x\ldots\ldots...\ldots..\ldots\text{Equation 3}[/tex]
Step 2: Substitute y with (125 - x) in Equation 1 and solve for x;
[tex]\begin{gathered} 45x+30(125-x)=4575 \\ 45x+3750-30x=4575 \\ 45x-30x=4575-3750 \\ 15x=825 \\ \frac{15x}{15}=\frac{825}{15} \\ x=55 \end{gathered}[/tex]
Since x = 55, therefore, the number of large boxes is 55
Step 3: Substitute x with 55 in Equation 3 and solve for y;
[tex]\begin{gathered} y=125-55 \\ y=70 \end{gathered}[/tex]
Since y = 70, therefore, the number of small boxes is 70
