Question

Solving a value mixture problem using a system of linear

Answer 1

We are given that there are 125 boxes. If "x" represents the number of larger boxes and "y" the smaller boxes then this is written mathematically as:

`x+y=125,(1)`

We are also given that the larger boxes weigh 45 pounds and the smaller boxes weigh 30 pounds each and the total weight is 4575 pounds. This is written mathematically as:

`45x+30y=4575,(2)`

We get a system of two equations and two variables. To solve the system we will use the method of elimination. To do that we will multiply equation (1) by -45, we get:

`-45x-45y=-5625`

Now, we add this equation to equation (2):

`-45x-45y+45x+30y=-5625+4575`

Now, we add like terms:

`-15y=-1050`

Now, we divide both sides by -15:

`y=-(1050)/(-15)`

Solving the operations:

`y=70`

Now, we substitute the value of "y" in equation (1):

`x+70=125`

Now, we subtract 70 from both sides:

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

Therefore, there are 55 larger boxes and 70 smaller boxes.