A collection of 108 coins containing only quarters and nickels is worth $21.
Coin Collection
\begin{tabular}{|r|c|c|c|}
\cline { 2 - 4 } \multicolumn{1}{c|}{} & \begin{tabular}{c} Number \\ of \\ Coins \end{tabular} & Value & Total \\
\hline Nickels & $n$ & 0.05 & $0.05 n$ \\
\hline Quarters & $q$ & 0.25 & $0.25 q$ \\
\hline Total & & & \\
\end{tabular}
Which value could replace $q$ on the chart?
A. 21
B. 108
C. $21-n$
D. $108-n$
Answer (2)
A device delivering a current of 15.0 A for 30 seconds results in 450 C of total charge. This charge corresponds to approximately 2.81 × 1 0 21 electrons flowing through the device. Thus, around 2.81 × 1 0 21 electrons flow during that time.
;
The total number of coins is expressed as n + q = 108 .
Solve for q in terms of n : q = 108 − n .
The expression that could replace q on the chart is 108 − n .
The final answer is 108 − n .
Explanation
Problem Analysis Let's analyze the problem. We have a collection of 108 coins that are either nickels or quarters. The total value of the collection is $21 . We are given a table with the number of nickels represented by n and the number of quarters represented by q . We need to find an expression that could replace q in the table.
Total Number of Coins We know that the total number of coins is 108, so we can write the equation: n + q = 108
Solving for q We want to find an expression for q in terms of n . To do this, we can solve the equation above for q :
q = 108 − n
Identifying the Correct Expression Now, let's check the given options to see which one matches our expression for q . The options are:
21
108
21 − n
108 − n
The expression we found for q is 108 − n , which matches the fourth option.
Final Answer Therefore, the value that could replace q on the chart is 108 − n .
Examples
Imagine you are managing a small store and need to keep track of your inventory. If you know the total number of items you have (e.g., 108 coins) and the number of one type of item (e.g., nickels), you can easily calculate the number of the other type of item (e.g., quarters) by subtracting the number of nickels from the total number of coins. This simple algebraic relationship helps you manage your inventory efficiently.
