Answered

Antoine and Tess have a disagreement over how to compute a $15\%$ gratuity on $\$46.00$.



Tess says, "It is easy to find $10\%$ of $46$ by moving the decimal point one place to the left to get $\$4.60$. Do that twice. Then add the two amounts to get $\$4.60 + \$4.60 = \$9.20$ for the $15\%$ gratuity."



How should Antoine respond to Tess's method?


A"Tess, you should use a table with $5\%$ segments to find the gratuity. Each $5\%$ segment has a value of $\$9.20$, so that is the $15\%$ gratuity."
B"Tess, the best way to find $15\%$ of $\$46.00$ is to multiply $0.015$ and $46.00$ to get $\$0.69$, which is the $15\%$ gratuity."
C"Tess, you found $20\%$ of the number because you added $10\%$ and $10\%$. You need to add $10\%$ to $\frac{1}{2}$ of $10\%$. Add $\$4.60$ and $\$2.30$ to get $\$6.90$, which is the $15\%$ gratuity."

Verified Answer :

  • Tess incorrectly calculated a 20% gratuity by adding 10% and 10%, instead of the desired 15%.
  • To find 15% correctly, calculate 10% of \(\$46.00\) (\(\$4.60\)) and 5% of \(\$46.00\) (\(\$2.30\)).
  • Summing these results (\(\$4.60 + \$2.30\)) gives the correct 15% gratuity of \(\$6.90\).
  • Antoine should choose the option: "Tess, you found 20% of the number because you added 10% and 10%. You need to add 10% to 1/2 of 10%. Add \$4.60 and \$2.30 to get \$6.90, which is the 15% gratuity."
  • The correct amount is \(\boxed{\$6.90}\).

Explanation

  1. Analyzing the Problem and Tess's Method

Tess wants to calculate a 15% gratuity on a bill of \$46.00. She calculates 10% of \$46.00 by moving the decimal point, which results in \$4.60. She then doubles this amount (\$4.60 + \$4.60 = \$9.20) to reach her final result. We need to evaluate her method, identify the error, and provide the correct calculation.

  1. Evaluating the Error

First, we calculate the correct 15% gratuity:
\[0.15 \times 46.00 = 6.90\]
Next, we evaluate Tess's result of \$9.20. Tess added 10% (\$4.60) to 10% (\$4.60), which is equivalent to calculating 20% of the total:
\[20\% \text{ of } 46.00 = 0.20 \times 46.00 = 9.20\]
Therefore, Tess accidentally calculated a 20% gratuity instead of the requested 15%.

  1. Correcting the Method and Identifying the Response

To find 15% correctly, we can break it down into 10% and 5%. We already know that 10% of \$46.00 is \$4.60. Since 5% is exactly half of 10%, we calculate:
\[5\% \text{ of } 46.00 = \frac{4.60}{2} = 2.30\]
Now, by adding these two components together, we obtain the correct 15% gratuity:
\[10\% + 5\% = 4.60 + 2.30 = 6.90\]
This confirms that the correct 15% gratuity on \$46.00 is \$6.90. Comparing this to the given options, the third option correctly identifies that Tess calculated 20% and provides the right method for calculating 15%.

Examples

Understanding percentages is vital in daily activities like dining out or shopping. When a server provides exceptional service, you might want to calculate a specific tip. By knowing how to mentally break down percentages (e.g., finding 10% and then halving it to find 5%), you can quickly and accurately compute values like a 15% tip on a bill of \(\$46.00\). This skill not only saves time but also ensures you are paying the correct amount, helping you manage your budget more effectively.

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