Lily sold 18 items at the street fair. She sold bracelets for $6 each and necklaces for $5 each for a total of $101. Which system of equations can be used to find $b$, the number of bracelets she sold, and $n$, the number of necklaces she sold?
$\begin{array}{l}
b+n=101 \\
6 b+5 n=18
\end{array}$
$\begin{array}{l}
b+n=101 \\
5 b+6 n=18
\end{array}$
$b+n=18$
$6 b+5 n=101$
$b+n=18$
$5 b+6 n=101$
Answer (2)
Establish the first equation based on the total number of items sold: b + n = 18 .
Establish the second equation based on the total revenue: 6 b + 5 n = 101 .
Combine these two equations to form the system of equations.
The system of equations that can be used to find the number of bracelets (b) and necklaces (n) Lily sold is { b + n = 18 6 b + 5 n = 101 .
Explanation
Forming the First Equation Let's analyze the given information to form the equations. We know that Lily sold a total of 18 items, which include bracelets and necklaces. Therefore, the sum of the number of bracelets ( b ) and the number of necklaces ( n ) is 18. This gives us our first equation:
First Equation b + n = 18
Forming the Second Equation We also know that bracelets were sold for $6 each and necklaces for $5 each, and the total revenue was $101. This means that the total revenue from bracelets ( 6 b ) plus the total revenue from necklaces ( 5 n ) equals $101. This gives us our second equation:
Second Equation 6 b + 5 n = 101
System of Equations Now, we combine these two equations to form the system of equations:
The System { b + n = 18 6 b + 5 n = 101
Finding the Correct Option Comparing this system of equations with the given options, we find that it matches the third option.
Conclusion Therefore, the correct system of equations is:
Final Answer { b + n = 18 6 b + 5 n = 101
Examples
Imagine you're organizing a school fundraiser where you're selling two types of items: t-shirts and mugs. You know the total number of items you sold and the total amount of money you raised. Setting up a system of equations, similar to Lily's situation, helps you determine exactly how many t-shirts and mugs you sold individually. This method is useful for inventory management, sales analysis, and financial planning in various real-world scenarios.
The correct system of equations for Lily's sales is { b + n = 18 6 b + 5 n = 101 . This represents the total number of items sold and the total revenue. The equations can be used to find the number of bracelets b and necklaces n she sold.
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