Nina is 10 years younger than Deepak. Deepak is 3 times as old as Nina. Which system of equations can be used to find $d$, Deepak's age, and $n$, Nina's age?
$\begin{array}{l}
d=n+10 \\
d=3 n
\end{array}$
$\begin{array}{l}
d=n-10 \\
d=3 n
\end{array}$
$\begin{array}{l}
d=n+10 \\
n=3 d
\end{array}$
$\begin{array}{l}
d=n-10 \\
n=3 d
\end{array}$
Answer (1)
Translate 'Nina is 10 years younger than Deepak' into an equation: d = n + 10 .
Translate 'Deepak is 3 times as old as Nina' into an equation: d = 3 n .
Combine the two equations to form the system: d = n + 10 and d = 3 n .
The correct system of equations is: d = n + 10 d = 3 n
Explanation
Problem Analysis Let's analyze the given information to form the equations.
We are given two pieces of information:
Nina is 10 years younger than Deepak.
Deepak is 3 times as old as Nina.
We need to translate these into equations using d for Deepak's age and n for Nina's age.
Forming the Equations The first statement, "Nina is 10 years younger than Deepak," means that Deepak's age is 10 more than Nina's age. This can be written as:
d = n + 10
The second statement, "Deepak is 3 times as old as Nina," means that Deepak's age is 3 times Nina's age. This can be written as:
d = 3 n
The System of Equations So, the system of equations that represents the given information is:
{ d = n + 10 d = 3 n
Identifying the Correct Option Comparing this to the given options, we see that the first option matches our system of equations.
Final Answer Therefore, the correct system of equations is:
d = n + 10 d = 3 n
Examples
Understanding systems of equations is crucial in many real-world applications. For instance, consider a scenario where you're trying to optimize a budget. Suppose you have a fixed amount of money to spend on two different items, and you know the relationship between the quantities and costs of these items. By setting up a system of equations, you can determine the optimal quantities of each item to purchase within your budget. This approach is widely used in economics, finance, and resource management to make informed decisions and achieve desired outcomes.
