Math Problem Statement
Solution
It looks like the problem involves a box containing 50 coins made up of pennies, dimes, and quarters, and their total value is $5.87. We also know that the number of pennies equals the number of dimes.
Let's break down the problem:
Variables:
- Let represent the number of pennies.
- Since the number of pennies equals the number of dimes, we can also say that the number of dimes is .
- Let represent the number of quarters.
Total number of coins:
The total number of coins is 50: This simplifies to:
Total value:
The total value of the coins is $5.87, or 587 cents. The value contributions are:
- Pennies:
- Dimes:
- Quarters:
The total value in cents is: Multiply the equation by 100 to get rid of the decimals: This simplifies to:
Solving the system of equations:
We now have two equations:
I'll solve this system of equations to find and .The solution to the system of equations is:
- (so there are 17 pennies and 17 dimes),
- (there are 16 quarters).
Breakdown:
- 17 pennies,
- 17 dimes,
- 16 quarters.
These add up to a total of 50 coins and a value of $5.87.
Would you like further clarification or more details on this? Here are five related questions you might want to explore:
- How would the solution change if the total value of the coins were different?
- How can we verify the total value using the number of pennies, dimes, and quarters?
- What if the number of dimes was twice the number of pennies?
- How would we solve the system if we only had the number of pennies and the total value?
- Can this method work for different combinations of coins (e.g., nickels instead of dimes)?
Tip: When solving word problems, always define your variables clearly and set up equations based on the conditions provided.
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Math Problem Analysis
Mathematical Concepts
Linear equations
Algebra
Formulas
2x + y = 50 (where x is the number of pennies/dimes and y is the number of quarters)
11x + 25y = 587 (converting total value into cents and solving the system of equations)
Theorems
System of linear equations
Suitable Grade Level
Grades 9-10
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