Question

O SYSTEMS OF EQUATIONS AND MATRICESSolving a value mixture problem using a system of linear...

Answer 1

Let the number of large boxes be

`=x`

Let the number of small boxes be

`=y`

The total number of boxes are

`=115`

The system of equation to represent this will be given below as

`x+y=115\ldots\ldots(1)`

The large box weigh

`55\text{ pounds each}`

The small box weigh

`20\text{ pounds each}`

The total weight of the boxes is

`=4575\text{ pounds}`

The system of the equation to represent this is

`55x+20y=4575\ldots\text{.}(2)`

Step 1:

From equation (1) make x the subject of the formula to form equation (3)

`\begin{gathered} x+y=115 \\ x=115-y\ldots\ldots(3) \end{gathered}`

Step 2:

substitute equation (3) in equation (2)

`\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} \\ (-35y)/(-35)=(-1750)/(-35) \\ y=50 \end{gathered}`

Substitute the value of y=50 in equation (3)

`\begin{gathered} x=115-y \\ x=115-50 \\ x=65 \end{gathered}`

Hence,

Number of large boxes = 65

Number of small boxes = 50