Final answer:
In a coin collection with nickels and quarters totaling 30 coins, where quarters outnumber nickels by 2, we use algebra to find that there are 14 nickels in the collection.
Step-by-step explanation:
The student is tasked with solving a problem regarding a coin collection that consists of nickels and quarters. To find the number of nickels in the collection, we first let the variable n represent the number of nickels. Since there are 30 coins in total and the number of quarters is 2 more than the number of nickels, we can express the number of quarters as n + 2. Setting up an equation, we add the number of nickels and quarters to equal the total number of coins:
n + (n + 2) = 30
Solving for n, we combine like terms:
2n + 2 = 30
Subtracting 2 from both sides gives us:
2n = 28
Dividing by 2, we find the number of nickels:
n = 14
Therefore, there are 14 nickels in the collection. Answer choice D is correct.