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# Use an inequality and the five-step process to solve each problem. An unconditional acceptance into the Master of Business Administration (MBA) program at Arkansas State University will be given to students whose GMAT score plus $200$ times the undergraduate grade point average is at least $950$. Robbin's GMAT score was $500$. What must her grade point average be in order to be unconditionally accepted into the program?

Solution

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$\textbf{\textcolor{#4257b2}{Familiarize}}$

We are looking for $\textbf{a number}$ which when multiplied by $200$ and added to $500$ gives at least $950$. We can denote the number as $\textcolor{#c34632}{x}$

$\textbf{\textcolor{#4257b2}{Translate}}$

$500+\boxed{\textcolor{#c34632}{x}}\cdot200\geq950$

$\textbf{\textcolor{#4257b2}{Carry out}}$

\begin{align*} 500+200x&\geq950\\ 200x&\geq950-500 \tag{\textcolor{#4257b2}{Addition principle.}}\\ 200x&\geq450\\ x&\geq\frac{450}{200} \tag{\textcolor{#4257b2}{Multiplication principle.}}\\ x&\geq\boxed{\textcolor{#c34632}{2.25}} \end{align*}

$\textbf{\textcolor{#4257b2}{Check}}$

\begin{align*} 3&\geq2.25\\ 500+\boxed{\textcolor{#c34632}{3}}\cdot200&\stackrel{?}{\geq}950\\ 1100&\geq950 \end{align*}

$\textbf{\textcolor{#4257b2}{State}}$

$\textbf{The number}$ is $\boxed{\textcolor{#c34632}{2.25}}$.

Her grade point average should be at least $\boxed{\textcolor{#c34632}{2.25}}$.

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