after earning interest, the balance of an account is 420. the balance is 7/6 of the original balance. how much interest did it earn.
Let's assume the original balance of the account is x.
The balance after earning interest is 7/6 of the original balance, so it is 7/6 * x = (7/6)x.
Since the balance after earning interest is 420, (7/6)x = 420.
To find the interest, we need to subtract the original balance from the balance after earning interest: (7/6)x - x = 420 - x.
Combining like terms, we have (7/6 - 1)x = 420 - x.
Simplifying further, we get (1/6)x = 420 - x.
Moving terms around, 420 - x = (1/6)x.
Adding x to both sides, we have 420 = (7/6)x.
Dividing both sides by (7/6), we get x = 360.
The interest earned is the difference between the balance after earning interest and the original balance: (7/6)x - x = 420 - 360 = 60.
Therefore, it earned 60 in interest.
To find out how much interest the account earned, we need to determine the original balance. Let's represent the original balance as "x".
According to the given information, the balance after earning interest is 420, which is 7/6 of the original balance:
420 = (7/6) * x
To find the value of x, we can rearrange the equation by multiplying both sides by 6/7:
6/7 * 420 = x
Simplifying the equation:
360 = x
Therefore, the original balance of the account was $360.
To calculate the interest earned, we can subtract the original balance from the final balance:
Interest earned = Final balance - Original balance
Interest earned = 420 - 360
Interest earned = $60