Question

Solve the following equation to determine when the costs are equal.3.25x+400=2.50x+600

Answer 1

Use the properties of equalities to solve for x:

$3.25x+400=2.50x+600$

We would like the terms which include the variable x to be on one single side of the equation, and the other terms on the other side. So, substract 2.50x from both sides:

$\begin{gathered} \Rightarrow3.25x+400-2.50x=2.50x+600-2.50x \\ \Rightarrow3.25x-2.50x+400=600 \\ \Rightarrow0.75x+400=600 \end{gathered}$

Next, substract 400 from both sides:

$\begin{gathered} \Rightarrow0.75x+400-400=600-400 \\ \Rightarrow0.75x=200 \end{gathered}$

Divide both sides by 0.75:

$\begin{gathered} \Rightarrow\frac{0.75x}{0.75}=\frac{200}{0.75} \\ \Rightarrow x=\frac{200}{3/4} \\ \Rightarrow x=\frac{4\times200}{3} \\ \Rightarrow x=\frac{800}{3} \\ \Rightarrow x\approx266.667 \end{gathered}$

Therefore:

$\begin{gathered} x=\frac{800}{3} \\ \approx266.667 \end{gathered}$