Question

The total bill for four friends eating at a restaurant (including tax) is $$\$ 36.00$$. The friends wish to add a \(20 \%\) tip and then to divide the bill evenly among the four of them. How much will each person pay? A. $$\$ 7.20$$ B. $$\$ 9.00$$ C. $$\$ 10.80$$ D. $$\$ 16.20$$

Short answer

Each person will pay $$\$ 10.80$$.

Step-by-step solution

Find the Tip Amount

We need to find 20% of the total bill, which is $36.00. To calculate 20% of a number, we multiply the number with 0.20 (since 20/100 = 0.20). \(Tip = 0.20 \times 36.00\)

Calculate the Tip Amount

Now, we will calculate the tip amount. \(Tip = 0.20 \times 36.00 = 7.20\)

Find the New Total Bill

After calculating the tip amount, we will add it to the total bill to find the new total bill. \(New\_Total\_Bill = Total\_Bill + Tip = 36.00 + 7.20\)

Calculate the New Total Bill

Now, we will calculate the new total bill. \(New\_Total\_Bill = 36.00 + 7.20 = 43.20\)

Find the Amount Each Person Pays

Now, we will divide the new total bill by the number of friends (4) to find out how much each person pays. \(Amount\_Each\_Person\_Pays = \frac {New\_Total\_Bill}{Number\_of\_Friends} = \frac {43.20}{4}\)

Calculate the Amount Each Person Pays

Now, we will calculate the amount each person pays. \(Amount\_Each\_Person\_Pays = \frac {43.20}{4} = 10.80\) The answer is \(10.80\). Each person will pay $10.80, so the correct answer is C. $$\$ 10.80$$.

Key concepts

Percentage Calculation

Mastering percentage calculations is crucial in various everyday situations, including financial planning, analysis, and even when dining out. To calculate a percentage of a number, we essentially need to convert the percentage into a decimal by dividing it by 100. This is because the word 'percent' literally means 'per hundred'.

For the math problem we're considering, finding a 20% tip on a $36.00 bill involves multiplying 36.00 by 0.20 (since 20% is equivalent to 20/100, which simplifies to 0.20). It's useful to understand this conversion process because it allows you to easily find any percentage of any number by using the multiplication operation. Consistently practicing this method will make you adept at quickly figuring out sales tax, discounts, interest rates, and tips without relying on a calculator.

Division of Expenses

Splitting costs among a group is a common scenario in daily life. Whether you're sharing a meal, dividing costs of shared services, or budgeting for a group event, understanding how to divide expenses fairly is extremely important.

To divide expenses evenly, simply sum up the total cost and then divide it by the number of individuals sharing the expense. In our math problem, after adding the tip to the original bill, the next step is dividing the new total by four—the number of friends. The concept of dividing expenses guarantees that each participant bears an equal portion of the costs, ensuring fairness and transparency in financial matters. This mathematical skill is a key part of personal finance and is also employed in various business contexts, including splitting profits, costs, and investments.

Tip Calculation

Being able to accurately calculate a tip is a social skill that reflects acknowledgement for service received. To compute a tip, first decide on the percentage of the total bill you wish to offer as a tip. Common percentages range around 15% to 20% for satisfactory to excellent service.

Once you have determined the percentage, convert it into decimal form and multiply it by the total bill amount to find the tip. Remember to add the calculated tip back to the original bill to find the new total amount that needs to be paid. In our exercise, the 20% tip shows appreciation for the service at the restaurant and is distributed evenly exactly like the rest of the bill, maintaining fairness among the friends.