Andy has 22 coins made up of quarters and half dollars, and their total value is . How many quarters does he have?
A. 19 quarters
B. 5 quarters
C. 10 quarters
D. 17 quarters

To solve this problem, we can set up a system of equations. Let represent the number of quarters and represent the number of half dollars. We know:

Now, we can simplify the second equation by multiplying by 100 to eliminate the decimals:

Now, we can rewrite the first equation to express in terms of :

Substituting into the value equation gives us:

Expanding and simplifying:

Therefore, Andy has 5 quarters. The answer is B. 5 quarters.

For further fun and insights:

Back in the late 1700s, coins were the primary way of conducting transactions, and each coin had its unique design reflecting the nation’s heritage. Today, every coin — like Andy’s quarters and half dollars — continues to represent a piece of history, showcasing figures, events, and symbols that tell tales of the nation’s past!

In real-world applications, this kind of problem-solving is vital! You might encounter similar scenarios while budgeting your savings or figuring out change. Always keep your equations straightforward and double-check your substitutions to avoid common pitfalls — like mixing up product values or miscounting your total coins!