Question
upstudy study bank question image url

Andy has 22 coins made up of quarters and half dollars, and their total value is \( \$ 9.75 \). How many quarters does he have? A. 19 quarters B. 5 quarters C. 10 quarters D. 17 quarters

Ask by Davison Nunez. in the United States
Mar 12,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Andy has 5 quarters.

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Mind Expander

To solve this problem, we can set up a system of equations. Let \( q \) represent the number of quarters and \( h \) represent the number of half dollars. We know: 1. The total number of coins is \( q + h = 22 \). 2. The total value of the coins is \( 0.25q + 0.50h = 9.75 \). Now, we can simplify the second equation by multiplying by 100 to eliminate the decimals: \[ 25q + 50h = 975. \] Now, we can rewrite the first equation to express \( h \) in terms of \( q \): \[ h = 22 - q. \] Substituting \( h \) into the value equation gives us: \[ 25q + 50(22 - q) = 975. \] Expanding and simplifying: \[ 25q + 1100 - 50q = 975, \] \[ -25q + 1100 = 975, \] \[ -25q = 975 - 1100, \] \[ -25q = -125, \] \[ q = \frac{125}{25} = 5. \] 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!

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy