Coin Algebra Word Problem Game

Coin Algebra Word Problem Quiz/Game
This game focuses on solving word problems involving Arithmetic Coin logic. Scroll down the page for a more detailed explanation.

 

 

How to Play the Coin Algebra Explorer Game

1. Look at the Problem: Read the problem carefully. Solve it and select one of the answers.
   
2. Check Your Work: If you selected the right answer, it will be highlighted in green. If you are wrong, it will be highlighted in red and the correct answer will be highlighted in green. A hint will be given to help you find the correct answer.
   
3. Get a New Problem: Click “Next Question” for a new problem.
   Your score is tracked, showing how many you’ve gotten right.
   
4. Finish Game When you have completed 10 questions, your final score will be displayed.
    
   

How to Solve Coin Algebra Word Problems
Coin word problems are a classic application of linear equations. The secret to solving them is understanding the difference between the number of coins (quantity) and the value of the coins (money).
The Core Variables
First, define your variables based on the coin names.
Let p = number of pennies
Let n = number of nickels
Let d = number of dimes
Let q = number of quarters

The Two-Equation System
Most problems require you to build two separate equations:
A. The Quantity Equation (How many?)
This equation only cares about the physical count of the items.
Total Count = p + n + d + q
B. The Value Equation (How much?)
This equation multiplies each coin by its monetary worth.
Total Value = 0.01p + 0.05n + 0.10d + 0.25q
(Pro tip: Multiply the whole equation by 100 to work in cents and avoid decimals)
100 × Total Value} = 1p + 5n + 10d + 25q

Step-by-Step Methodology
Step 1: Define Relationships
Look for phrases like “twice as many dimes as nickels."
This means: d = 2n
Step 2: Set up the Value Equation
Write the equation using the values (1, 5, 10, 25).
Step 3: Substitution
Replace variables so you only have one type of variable left. If d = 2n, replace every d in your value equation with (2n).
Step 4: Solve and Verify
Solve for the first variable, then plug it back in to find the others. Always check if the final counts add up to the total value mentioned in the problem.

Example Walkthrough
Problem: “Sarah has $2.10 in nickels and dimes. She has 3 more dimes than nickels. How many of each does she have?”
Identify Relationships: Let n = number of nickels.
Dimes (d) = n + 3.
Set up the Value Equation (in cents):
5n + 10d = 210
Substitute:
5n + 10(n + 3) = 210
Solve:
5n + 10n + 30 = 210
15n = 180
n = 12
Find the other coin:
d = 12 + 3 = 15

Check:
12 nickels ($0.60) + 15 dimes ($1.50) = $2.10.
 

This video gives a clear, step-by-step approach to explain how to solve coin algebra word problems.

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