Fred is

Question

\[4\] times as old as Nathan and is also
\[27\] years older than Nathan.
Let
\[f\] be Fred's age and let
\[n\] be Nathan's age.
Which system of equations represents this situation?
Choose 1 answer:
Choose 1 answer:
(Choice A)

\[\begin{cases}
f=4n \\\\
f=n+27
\end{cases}\]
A

\[\begin{cases}
f=4n \\\\
f=n+27
\end{cases}\]
(Choice B)

\[\begin{cases}
4f=n \\\\
f=n+27
\end{cases}\]
B

\[\begin{cases}
4f=n \\\\
f=n+27
\end{cases}\]
(Choice C)

\[\begin{cases}
n=4f \\\\
n=f+27
\end{cases}\]
C

\[\begin{cases}
n=4f \\\\
n=f+27
\end{cases}\]
(Choice D)

\[\begin{cases}
f=4n \\\\
f=n-27
\end{cases}\]
D

\[\begin{cases}
f=4n \\\\
f=n-27
\end{cases}\]

Answer 1

To set up the correct system of equations representing the situation involving Fred's and Nathan's ages, we translate the given statements into mathematical expressions.

1. "Fred is 4 times as old as Nathan" translates to: \[ f = 4n \] where \( f \) is Fred's age and \( n \) is Nathan's age.

2. "Fred is also 27 years older than Nathan" translates to: \[ f = n + 27 \]

Putting these two equations together, we have: \[ \begin{cases} f = 4n \ f = n + 27 \end{cases} \]

Now, let's look at the choices available:

• Choice A: \[ \begin{cases} f = 4n \ f = n + 27 \end{cases} \]

• Choice B: \[ \begin{cases} 4f = n \ f = n + 27 \end{cases} \]

• Choice C: \[ \begin{cases} 4f = n \ f = n + 27 \end{cases} \]

• Choice D: \[ \begin{cases} f = 4n \ f = n - 27 \end{cases} \]

The correct choice that represents the situation is Choice A: \[ \begin{cases} f = 4n \ f = n + 27 \end{cases} \]