60% of a bank account is $2,400. Find the full amount in the account.
The Correct Answer and Explanation is:
To find the full amount in the account when 60% of it equals $2,400, we need to determine the total value of the account. Let’s break this down step by step:
Step 1: Understand the problem
We are told that 60% of the total bank account amount equals $2,400. This means that 60% of the total amount (which we will call “X”) is $2,400. Mathematically, this relationship can be written as:
[
60\% \times X = 2400
]
Step 2: Convert percentage to decimal form
To work with percentages in equations, we convert 60% into decimal form. To do this, divide 60 by 100:
[
60\% = \frac{60}{100} = 0.60
]
So the equation becomes:
[
0.60 \times X = 2400
]
Step 3: Solve for X
Now, to find the full amount (X), we need to isolate X. To do that, divide both sides of the equation by 0.60:
[
X = \frac{2400}{0.60}
]
Step 4: Perform the division
Performing the division:
[
X = \frac{2400}{0.60} = 4000
]
Step 5: Conclusion
The full amount in the bank account is $4,000.
Explanation
This problem is an example of how to find the total value when given a percentage of that value. The key idea is recognizing that 60% of the total account value equals $2,400. By using algebra to set up an equation and then solving for the unknown (the total amount), we can determine the full value. The percentage form of 60% is 0.60, which we use in the equation (0.60 \times X = 2400). Dividing both sides by 0.60 allows us to isolate X and find that the total amount in the bank account is $4,000.