Verified Answer :
- The total bill is calculated by adding the base bill of \(\$11.72\) to the 20% tip, which is \(0.2 \times 11.72\).
- This gives the first correct expression: \(11.72 + [(0.2)(11.72)]\).
- Factoring the expression gives \(11.72(1 + 0.2) = 1.2(11.72)\), which is the second correct expression.
- \(\boxed{11.72 + [(0.2)(11.72)] \text{ and } 1.2(11.72)}\)
Explanation
- Analyzing the Bill and Tip Calculation
The problem asks us to determine the total bill amount after adding a 20% tip to a base bill of \(\$11.72\).
First, let's identify the components of the total bill.
- The base amount of the meal is \(P = \$11.72\).
- The tip amount is calculated as 20% of the base amount: \(\text{Tip} = 0.20 \times P = 0.20 \times 11.72\).
- The total bill \(B\) is the sum of the base amount and the tip: \(B = P + \text{Tip}\).
By substituting the base amount into the expression for the total bill, we get:
\[B = 11.72 + (0.2 \times 11.72)\]
This matches the second expression listed in the problem.
Furthermore, we can factor the expression \(B = P + 0.2P\) as:
\[B = P(1 + 0.2) = 1.2P = 1.2 \times 11.72\]
This is another mathematically equivalent way to express the total bill. Since the request asks for two correct expressions, these two forms—the explicit sum and the factored version—are the standard ways to represent the final amount. Note that \((0.2)(11.72)\) only represents the tip amount, and \(11.72 - [(0.2)(11.72)]\) would represent a discount rather than a tip.
- Identifying the Correct Expressions
We have examined the options provided. The expression \(11.72 + [(0.2)(11.72)]\) clearly represents adding 20% of the base bill to the base bill itself. As derived, the equivalent factored expression is \(1.2(11.72)\). Therefore, these are the two correct expressions for the total bill. The other listed options represent either just the tip amount or a subtraction, which does not apply to a gratuity. Consequently, the correct expressions for the total bill are \(11.72 + [(0.2)(11.72)]\) and \(1.2(11.72)\).
Examples
Understanding how to calculate tips and total bills is a valuable life skill for dining out or handling customer service expenses. For example, if you are at a restaurant and the bill is \(\$45.00\) and you want to leave a 15% tip, you can calculate the total as \(\$45 + (0.15 \times 45)\) or simply \(\$45 \times 1.15 = \$51.75\). Mastering these percentage calculations ensures you can quickly and accurately determine total costs in various everyday transactions.