Question

MetroTran had a route reduction and lost 1/5 of its routes. If 88 of its routes were left after the reduction, how many routes were there originally?

Answer 1

Step 1: Represent the total original routes with an unknown

Let the total original route be x

Step 2: Represent the first statement with a mathematical expression

$\begin{gathered} \text{The loss is 1/5} \\ \text{loss}=\frac{1}{5}\times x \end{gathered}$

Step 3: Find the expression for the remaining routes

$\begin{gathered} \text{Routes left after loss} \\ x-\frac{1}{5}\times x=x-\frac{x}{5}=\frac{5x-x}{5}=\frac{4x}{5} \end{gathered}$

Step 4: Equate the expression for the remaining routes to the given statement in the question

$\frac{4x}{5}=88$

Step 5: Solve the equation to get x

$\begin{gathered} \frac{4x}{5}=88 \\ 4x=5\times88 \\ x=\frac{5\times88}{4} \\ x=5\times22 \\ x=110 \end{gathered}$

Hence