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:

$y=-\frac{1050}{-15}$

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.