Full solution

Q. Isabella paid one of her bills late and owed a

4\%

late fee. Her total, with the late fee, was

\$780

. How much was Isabella's original bill in dollars?

\newline

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Understand Total Paid: We know: $\newline$ Total amount paid with late fee: $\$780$ $\newline$ Late fee percentage: $4\%$ $\newline$ To find the original bill amount, we need to understand that the total amount paid is $104\%$ of the original bill ( $100\%$ of the bill + $4\%$ late fee). $\newline$ Let's represent the original bill amount as $x$ . $\newline$ So, $104\%$ of $x$ is equal to $\$780$ . $\newline$ We can write this as $1.04x = \$780$ . $\newline$ Now, we need to solve for $x$ to find the original bill amount.
Represent Original Amount: To solve for $x$ , we divide both sides of the equation by $1.04$ . $x = \frac{\$(780)}{1.04}$ Now, we perform the division to find the value of $x$ . $x = \$(750)$ This means the original bill amount was $\$(750)$ .
Solve for Original Amount: We should check our math to ensure there are no errors. $\newline$ Let's calculate $4$ \% of $\$750$ to see if it adds up to the late fee that would result in the total of $\$780$ . $\newline$ $4$ \% of $\$750$ is $0.04 \times \$750 = \$30$ . $\newline$ Now, we add the late fee to the original bill amount to see if it matches the total amount paid. $\newline$ $\$750 + \$30 = \$780$ $\newline$ This confirms that our calculation is correct.