Solve System of Equations for Dimes and Quarters

Math Problem Statement

Jasmine saves some dimes and quarters. She has 40 coins in her coin bank, which total up to $6.55. How many of each coin does she have?

The problem from the image is:

Jasmine saves some dimes and quarters. She has 40 coins in her coin bank, which total up to $6.55. How many of each coin does she have?

Let's define two variables to represent the unknowns:

From the problem, we can set up two equations:

The total number of coins is 40: $d + q = 40$
The total value of the coins is $6.55, which is 655 cents. The value of a dime is 10 cents, and the value of a quarter is 25 cents: $10d + 25q = 655$

We now have a system of two equations:

1. \ d + q &= 40 \\ 2. \ 10d + 25q &= 655 \end{aligned}$$ I will solve this system of equations.The solution to the system is: - Jasmine has **23 dimes**. - Jasmine has **17 quarters**. Would you like more details about how this solution was reached or have any further questions? Here are 5 related questions to expand on this topic: 1. How do we solve systems of equations using substitution? 2. What are other methods to solve systems of linear equations (e.g., elimination)? 3. How would the solution change if Jasmine had fewer or more total coins? 4. Can you solve the problem if Jasmine had nickels instead of dimes? 5. How do different coin combinations affect the total amount of money? **Tip:** When solving systems of equations, make sure the units (e.g., cents versus dollars) are consistent to avoid confusion.

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Algebra
Systems of Linear Equations

d + q = 40
10d + 25q = 655

Solving Systems of Linear Equations

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