Final answer:
The total cost of a meal can be found using the formula C = C_0 + (C_0 × x) + (C_0 × t), where C is the total cost, C_0 is the original cost, x is the tax rate, and t is the tip rate. To solve for the tip rate, the formula is rearranged to t = (C - C_0 - (C_0 × x)) / C_0.
Step-by-step explanation:
Finding Total Bills Involving Tips and Taxes
To write a formula for the total cost of a meal 'C' in terms of the original cost of the meal 'C_0', the meal tax rate 'x' written as a decimal, and the tip rate 't' also written as a decimal, you would add both the tax and the tip to the original cost. The formula would be: C = C_0 + (C_0 × x) + (C_0 × t).
For example, if Jerod's restaurant bill is $47.50 with a 6% sales tax and a desired tip rate, then the tax added to the bill would be 0.06 × $47.50 = $2.85. If they decide to leave an 18% tip, you would calculate the tip amount as 0.18 × $47.50.
Solving for the Tip Rate 't'
If you have a given total cost 'C', original cost 'C_0', and meal tax rate 'x', you can rearrange the initial formula to solve for the tip rate 't'. This would be done by subtracting the tax from the total cost, then subtracting the original cost, and finally dividing by the original cost. The formula to solve for 't' is: t = (C - C_0 - (C_0 × x)) / C_0.