Question

If Steve had 133 total coins of nickels, dimes, and quarters, with three times as many dimes as quarters, how many of each type of coin did he save?

A) Nickels: 19, Dimes: 57, Quarters: 57
B) Nickels: 33, Dimes: 66, Quarters: 34
C) Nickels: 57, Dimes: 19, Quarters: 57
D) Nickels: 66, Dimes: 33, Quarters: 34

Answer 1

To determine how many of each type of coin Steve has, it is necessary to use simple algebra to set equations based on the given conditions. Only one set of numbers from the provided options adheres to these conditions and adds up to 133 coins in total, which is Option B: Nickels: 33, Dimes: 66, Quarters: 34.

Step-by-step explanation:

The question involves combinatorics and basic arithmetic to solve for the number of nickels, dimes, and quarters Steve has. Given that the total number of coins is 133 and there are three times as many dimes as quarters, we can set up the following equations:

1. Let the number of quarters be q.
2. The number of dimes will then be 3q because there are three times as many dimes as quarters.
3. We can express the number of nickels as 133 - q - 3q because the total number of coins is 133.
4. Combining the numbers of nickels, dimes, and quarters, we get 133 = n + d + q which simplifies to 133 = n + 3q + q or 133 = n + 4q.
5. Using the options given, the only combination where 3q is an integer and the total counts add up to 133 is Option B: Nickels: 33, Dimes: 66, Quarters: 34.

Therefore, Steve has 33 nickels, 66 dimes, and 34 quarters.