Shane returned from a trip to Las Vegas with $\$ 300.00$ , which was $50 \%$ more money than he had at the beginning of the trip. How much money did Shane have at the beginning of his trip?

Solution

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Step 1

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$\textbf{Step 1: Read and list.}$

$\textit{Known items:}$ The final amount of money Shane has is $300 which was 50% more money than the initial amount of money he had. \

\textit{Unknown items:} Initial amount of money Shane had at the beginning of his trip.\

\textbf{Step 2: Assign a variable and translate information.}\

Let $x$ be the initial amount of money Shane had at the beginning of his trip.\

\textbf{Step 3: Reread and write an equation.}\

$300 is 50% more than the initial amount of money Shane had.\ [300=x+0.5x]

\textbf{Step 4: Solve the equation.}\

Combine similar terms on the right side: [300=1.5x] Divide both sides by 1.5: [200=x]

\textbf{Step 5: Write the answer.}\$$\color{#c34632}{\text{Shane had $200 at the beginning of his trip.}}\

\textbf{Step 6: Reread and check.}\

50% of $200 is $100. $\$200+\$100=\$300$ which confirms our answer.

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