Final answer:
The customer left a $1.40 tip which was 20% of the total cost after tax. We use algebra to calculate the pre-tax and pre-tip total as approximately $5.83, and then find the final total by adding tax and tip to get approximately $7.52.
Step-by-step explanation:
Finding Total Bills Involving Tips and Taxes
The question involves calculating the total cost of a meal at a restaurant including tips and taxes. Since the customer left a $1.40 tip, and this represents 20% of the total cost after including the tax, we first need to establish the total cost before the tip. Given that the tax is at a rate of 5%, we can set up an equation to solve for the pre-tip amount (let's call it x).
First, calculate the total amount including tax:
x + 0.05x = 1.2x (total cost with tax)
Since the tip is 20% of the total cost including tax, the equation is:
0.20 × 1.2x = $1.40
Solve for x to find the pre-tax and pre-tip total:
0.20 × 1.2x = $1.40x
= $1.40 / (0.20 × 1.2)x
= $5.83 (approximate pre-tax and pre-tip total)
Now, add the tax to find the total before the tip:
$5.83 + (0.05 × $5.83) = $6.12 (approximate total with tax before tip)
Lastly, the final total including the tip is already given as the pre-tip total plus $1.40:
$6.12 + $1.40 = $7.52 (final total)