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(0.75x)/(0.75)=(200)/(0.75) \\ \Rightarrow x=(200)/(3/4) \\ \Rightarrow x=(4*200)/(3) \\ \Rightarrow x=(800)/(3) \\ \Rightarrow x\approx266.667 \end{gathered}`

Therefore:

`\begin{gathered} x=(800)/(3) \\ \approx266.667 \end{gathered}`