Lawanda and Sierra eat dinner at a restaurant with a 5.5% sales tax. They leave a 15% tip on the pre-tax amount of the bill.
If they pay a total of $40 including tax and tip, what was the pre-tax bill for their meal?
Let x be the pre-tax bill for their meal.
The sales tax is x * 5.5% = 0.055 * x.
The tip is 0.15 * x.
The total amount paid is x + 0.055x + 0.15 * x = $40.
The total amount can be written as 1.205 * x = $40.
Thus, the pre-tax bill for their meal is x = $40 / 1.205 = $33.1955 (approximated to the nearest cent).
Therefore, the pre-tax bill for their meal was approximately $33.20. Answer: \boxed{33.20}.
To find the pre-tax bill for Lawanda and Sierra's meal, we need to subtract the tax and tip from the total amount they paid.
Let's start by finding the tax amount. We know that the sales tax rate is 5.5% and the total amount paid is $40.
To calculate the tax, we can set up an equation:
Tax = Total Amount * Tax Rate
Tax = $40 * 5.5%
Dividing 5.5% by 100 will give us the decimal form of the tax rate, which is 0.055.
Tax = $40 * 0.055
Tax = $2.20
Now let's find the tip amount. We know that they left a 15% tip on the pre-tax amount.
To calculate the tip, we can again use an equation:
Tip = Pre-Tax Amount * Tip Rate
We don't know the pre-tax amount yet, but we can use a variable to represent it. Let's call it x.
Tip = x * 15%
Dividing 15% by 100 will give us the decimal form of the tip rate, which is 0.15.
Tip = x * 0.15
Now, the total amount paid can be expressed as:
Total Amount = Pre-Tax Amount + Tax + Tip
Using the values we have, we can substitute them in the equation:
$40 = x + $2.20 + Tip
Since we have an equation with two variables, we need another equation to solve for both x and Tip.
The tip amount can be calculated as:
Tip = x * 0.15
We can substitute this into the first equation:
$40 = x + $2.20 + (x * 0.15)
Now, let's simplify this equation to solve for x:
$40 = x + $2.20 + 0.15x
Combining like terms:
$40 = 1.15x + $2.20
Subtracting $2.20 from both sides:
$40 - $2.20 = 1.15x
$37.80 = 1.15x
Now, divide both sides of the equation by 1.15 to solve for x:
x = $37.80 / 1.15
x ≈ $32.87
Therefore, the pre-tax bill for Lawanda and Sierra's meal was approximately $32.87.