Question

You are deciding between First National Bank and Liberty Bank. They both offer checking and savings accounts. First National charges a $10 fee to receive checks and charges $2.50 per ATM transaction. Liberty Bank has no check fee but charges $3.25 per ATM transaction. How many times do you need to be charged an ATM fee before you are paying the same amount of money in fees at both banks?

Step 1: Define your variables - Look at the question statement. What are you being asked to find?



Step 2: Write 2 equations that use those unknown variables



Step 3: Solve the system of equations



Step 4: State your solution. What does it mean in the context of the word problem?

Answer 1

To find out how many times you need to be charged an ATM fee before you are paying the same amount of money in fees at both banks, set up a system of equations and solve for the number of ATM transactions.

Step-by-step explanation:

To find out how many times you need to be charged an ATM fee before you are paying the same amount of money in fees at both banks, we can set up a system of equations.

Let x be the number of ATM transactions.

For First National Bank, the total fee is $10 for receiving checks plus $2.50 per ATM transaction, so the equation is: y1 = 10 + 2.50x.

For Liberty Bank, the total fee is $3.25 per ATM transaction, so the equation is: y2 = 3.25x.

Now, we need to find the number of ATM transactions when the total fees are equal:

y1 = y2

10 + 2.50x = 3.25x

Subtracting 10 from both sides:

2.50x = 3.25x - 10

Subtracting 2.50x from both sides:

0.75x = 10

Dividing both sides by 0.75:

x = 10 / 0.75

x = 13.33

Since we cannot have a fraction of an ATM transaction, we round up to the nearest whole number.

Therefore, you need to be charged an ATM fee 14 times before you are paying the same amount of money in fees at both banks.