Yolanda paid for her movie ticket using 28 coins, all nickels and quarters. The ticket cost $4. Which system of linear equations can be used to find the number of nickels, \(n\), and the number of quarters, \(q\), Yolanda used?
\begin{array}{l}
n+q=28 \
0.05 n+0.25 q=4
\end{array}
\begin{array}{l}
n+q=4 \
5 n+25 q=28
\\
\end{array}
n+q=28
5 n+25 q=4
n+q=4
0.05 n+0.25 q=28
Answer (2)
Define n as the number of nickels and q as the number of quarters.
Write the equation for the total number of coins: n + q = 28 .
Write the equation for the total value of the coins: 0.05 n + 0.25 q = 4 .
The system of equations is: { n + q = 28 0.05 n + 0.25 q = 4 . The answer is the first option.
Explanation
Problem Analysis Let's analyze the problem. We know that Yolanda used 28 coins in total, which are a combination of nickels and quarters. We also know that the total value of these coins is $4 . We need to set up a system of equations that represents this situation, where n represents the number of nickels and q represents the number of quarters.
Equation for Total Number of Coins The first equation will represent the total number of coins. Since Yolanda used 28 coins in total, we can write this as: n + q = 28
Equation for Total Value of Coins The second equation will represent the total value of the coins. Each nickel is worth $0.05 and each quarter is worth $0.25 . The total value is $4 . So, we can write this as: 0.05 n + 0.25 q = 4
The System of Equations Therefore, the system of equations that represents this situation is:
{ n + q = 28 0.05 n + 0.25 q = 4
Identifying the Correct Option Comparing this to the given options, we see that the first option matches our system of equations.
Final Answer Thus, the correct system of equations is:
{ n + q = 28 0.05 n + 0.25 q = 4
Examples
Imagine you're running a lemonade stand and need to keep track of your earnings. You know you have a certain number of nickels and dimes, and you know the total amount of money you have. Setting up a system of equations like this helps you figure out exactly how many of each coin you have, so you can manage your money effectively. This is useful for budgeting, accounting, and making sure you're giving the correct change to your customers. Understanding how to create and solve these systems can help you in many real-world financial situations.
The correct system of equations representing Yolanda's situation is: n + q = 28 and 0.05 n + 0.25 q = 4 . This corresponds to the first option provided. By defining n as nickels and q as quarters, we can keep track of both the total number of coins and their total value.
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