Math Problem Statement
Len bought 2 postcards and received $1.35 in change in quarters and dimes. If he got 6 coins back, how many of each coin did he get?
Solution
Let's denote the number of quarters as and the number of dimes as .
We know the following:
- Len received a total of 6 coins:
- The total value of the coins is $1.35, which is 135 cents:
We now have a system of equations:
q + d &= 6 \quad \text{(1)} \\ 25q + 10d &= 135 \quad \text{(2)} \end{aligned}$$ ### Step 1: Simplify equation (2) We can simplify equation (2) by dividing everything by 5: $$5q + 2d = 27 \quad \text{(3)}$$ ### Step 2: Solve the system of equations We can solve the system using substitution or elimination. Let's use substitution: From equation (1), solve for $$d$$: $$d = 6 - q$$ Substitute this into equation (3): $$5q + 2(6 - q) = 27$$ Expand and simplify: $$5q + 12 - 2q = 27$$ $$3q + 12 = 27$$ $$3q = 15$$ $$q = 5$$ ### Step 3: Find $$d$$ Using $$q = 5$$ in equation (1): $$5 + d = 6$$ $$d = 1$$ ### Conclusion: Len received 5 quarters and 1 dime. Would you like a detailed explanation or have any further questions? Here are 5 related questions to explore further: 1. How much change would Len have received if he got 7 coins instead? 2. What if Len received 3 quarters and 3 dimes? How much change would that be? 3. How can you determine the possible combinations of coins if he received $2.35 instead? 4. What is the total value of coins if he received 4 quarters and 2 dimes? 5. How would the problem change if Len received nickels instead of dimes? **Tip:** When solving systems of equations, always check if you can simplify first, as this makes calculations easier!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Systems of Linear Equations
Coin Problems
Formulas
Linear equations
Theorems
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Suitable Grade Level
Grades 7-9