Question

Please help See attached photoWorking with system of linear problems

Answer 1

Number of large boxes: 55

Number of small boxes: 70

Step-by-step 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;

`\begin{gathered} 45x+30y=4575\ldots\ldots\ldots\text{Equation 1} \\ x+y=125\ldots\ldots.\ldots.\ldots\text{Equation 2} \end{gathered}`

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;

`y=125-x\ldots\ldots...\ldots..\ldots\text{Equation 3}`

Step 2: Substitute y with (125 - x) in Equation 1 and solve for x;

`\begin{gathered} 45x+30(125-x)=4575 \\ 45x+3750-30x=4575 \\ 45x-30x=4575-3750 \\ 15x=825 \\ (15x)/(15)=(825)/(15) \\ x=55 \end{gathered}`

Since x = 55, therefore, the number of large boxes is 55

Step 3: Substitute x with 55 in Equation 3 and solve for y;

`\begin{gathered} y=125-55 \\ y=70 \end{gathered}`

Since y = 70, therefore, the number of small boxes is 70