Sammie Took $$ 25$ Out Of Her Checking Account. After Taking The Money Out, She Had $$ 100$ Remaining. Which Equation Can Be Used To Find The Amount, $c$, Sammie Had In Her Account Before She Took The Money

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Understanding the Problem

Sammie took $25 out of her checking account, and after doing so, she had $100 remaining. We need to find the initial amount, denoted as cc, that Sammie had in her account before taking the money out.

Setting Up the Equation

To solve for the initial amount, we can use a simple algebraic equation. Let's denote the initial amount as cc. Since Sammie took $25 out of her account, the amount remaining is c−25c - 25. We are given that the remaining amount is $100. Therefore, we can set up the equation:

c−25=100c - 25 = 100

Solving the Equation

To solve for cc, we need to isolate the variable on one side of the equation. We can do this by adding 25 to both sides of the equation:

c−25+25=100+25c - 25 + 25 = 100 + 25

This simplifies to:

c=125c = 125

Interpreting the Result

The equation c=125c = 125 tells us that Sammie had $125 in her checking account before taking $25 out. This means that the initial amount, cc, is equal to $125.

Alternative Equation

We can also express the equation in a different form. Instead of using the equation c−25=100c - 25 = 100, we can use the equation:

c=100+25c = 100 + 25

This equation is equivalent to the original equation and also gives us the same result: c=125c = 125.

Conclusion

In this article, we have seen how to solve for the initial amount in Sammie's checking account. We set up an equation using the given information and solved for the variable cc. The result is that Sammie had $125 in her account before taking $25 out.

Real-World Applications

This type of problem can be applied to real-world situations, such as:

  • Banking: When a customer withdraws money from their account, the bank needs to update the account balance. This can be done using an equation like the one we solved.
  • Personal Finance: When managing personal finances, it's essential to keep track of income and expenses. This can be done by setting up equations like the one we solved to find the initial amount in an account.
  • Mathematical Modeling: Equations like the one we solved can be used to model real-world situations, such as population growth or chemical reactions.

Tips and Variations

  • Multiple Withdrawals: If Sammie had made multiple withdrawals from her account, we would need to set up a system of equations to solve for the initial amount.
  • Deposits: If Sammie had made deposits into her account, we would need to add the deposit amount to the initial amount to find the new balance.
  • Interest: If Sammie's account earned interest, we would need to take into account the interest rate and the time period to find the new balance.

Common Mistakes

  • Forgetting to Add or Subtract: When solving equations, it's essential to remember to add or subtract the correct values.
  • Not Isolating the Variable: When solving equations, it's essential to isolate the variable on one side of the equation.
  • Not Checking Units: When solving equations, it's essential to check the units to ensure that they are correct.

Conclusion

In this article, we have seen how to solve for the initial amount in Sammie's checking account. We set up an equation using the given information and solved for the variable cc. The result is that Sammie had $125 in her account before taking $25 out. This type of problem can be applied to real-world situations, such as banking, personal finance, and mathematical modeling.

Q: What is the initial amount in Sammie's checking account?

A: The initial amount in Sammie's checking account is $125.

Q: How do I set up the equation to solve for the initial amount?

A: To set up the equation, you need to use the given information that Sammie took $25 out of her account and had $100 remaining. The equation is:

c−25=100c - 25 = 100

Q: How do I solve the equation to find the initial amount?

A: To solve the equation, you need to add 25 to both sides of the equation:

c−25+25=100+25c - 25 + 25 = 100 + 25

This simplifies to:

c=125c = 125

Q: What if Sammie had made multiple withdrawals from her account?

A: If Sammie had made multiple withdrawals from her account, you would need to set up a system of equations to solve for the initial amount. For example, if she had withdrawn $25 and then $50, you would need to set up two equations:

c−25=100c - 25 = 100 c−50=75c - 50 = 75

Q: What if Sammie's account earned interest?

A: If Sammie's account earned interest, you would need to take into account the interest rate and the time period to find the new balance. The equation would be:

c+(c×r×t)=125c + (c \times r \times t) = 125

Where cc is the initial amount, rr is the interest rate, and tt is the time period.

Q: What are some common mistakes to avoid when solving for the initial amount?

A: Some common mistakes to avoid when solving for the initial amount include:

  • Forgetting to add or subtract the correct values
  • Not isolating the variable on one side of the equation
  • Not checking units to ensure that they are correct

Q: Can I use this method to solve for the initial amount in any type of account?

A: Yes, you can use this method to solve for the initial amount in any type of account, such as a savings account, a checking account, or a credit card account.

Q: Are there any variations of this problem that I should be aware of?

A: Yes, there are several variations of this problem that you should be aware of, including:

  • Multiple deposits or withdrawals
  • Interest earned on the account
  • Fees or charges associated with the account

Q: How can I apply this method to real-world situations?

A: You can apply this method to real-world situations such as:

  • Banking: When a customer withdraws money from their account, the bank needs to update the account balance.
  • Personal finance: When managing personal finances, it's essential to keep track of income and expenses.
  • Mathematical modeling: Equations like the one we solved can be used to model real-world situations, such as population growth or chemical reactions.

Q: What are some tips for solving for the initial amount?

A: Some tips for solving for the initial amount include:

  • Read the problem carefully and make sure you understand what is being asked.
  • Set up the equation using the given information.
  • Solve the equation by adding or subtracting the correct values.
  • Check your units to ensure that they are correct.

Q: Can I use this method to solve for the initial amount in a joint account?

A: Yes, you can use this method to solve for the initial amount in a joint account. However, you will need to take into account the fact that the account is joint and that both parties have access to the funds.

Q: Are there any online resources that I can use to help me solve for the initial amount?

A: Yes, there are several online resources that you can use to help you solve for the initial amount, including:

  • Online calculators
  • Math websites
  • Online tutoring services

Q: Can I use this method to solve for the initial amount in a business account?

A: Yes, you can use this method to solve for the initial amount in a business account. However, you will need to take into account the fact that the account is business-related and that there may be additional fees or charges associated with the account.