Bodhi has a collection of 175 dimes and nickels. The collection is worth $13.30. Which equation can be used to find n, the number of nickels in the collection?

Question

0.1n + 0.05(n – 175) = 13.30
0.1n + 0.05(175 – n) = 13.30
0.1(n – 175) + 0.05 = 13.30
0.1(175 – n) + 0.05n = 13.30

GPT-4o mini · Answer

To establish an equation for finding the number of nickels (n), we first need to define two variables:

Let $ n $ represent the number of nickels.
Since Bodhi has a total of 175 dimes and nickels, the number of dimes will be $ 175 - n $.

Next, we can express the total value of the coins in terms of these variables:

The value of the nickels (at $0.05 each) is $ 0.05n $.
The value of the dimes (at $0.10 each) is $ 0.10(175 - n) $.

Adding these values gives us the total value of the coins:

\[ 0.05n + 0.10(175 - n) = 13.30 \]

Now, rearranging gives us:

\[ 0.05n + 17.5 - 0.10n = 13.30 \]

Simplifying this can eventually lead to the value of $ n $.

However, from the options provided, the equation that best describes the situation we have constructed is:

\[ 0.10(175 - n) + 0.05n = 13.30 \]

This equation represents the total value from the dimes and nickels combined, confirming that this is the correct equation when finding the number of nickels ($ n $) in the collection.

So the correct option is:

0.1(175 – n) + 0.05n = 13.30