Jackie has a prescription for 100 pills to be taken, one every 8 hours, at 7 a.m., 3 p.m., and...

1. Translate the problem requirements: Jackie needs to take 100 pills total, with 3 pills per day (at 7 a.m., 3 p.m., and 11 p.m.). Starting at 3 p.m. on July 1, we need to find when the 100th pill is taken.
2. Calculate total days needed: Determine how many complete days are required and account for any partial days based on the timing pattern.
3. Track the progression from start date: Count forward from July 1 at 3 p.m. through the calculated number of days to find the final date and time.
4. Identify the specific timing of the last pill: Determine which time slot (7 a.m., 3 p.m., or 11 p.m.) the 100th pill falls on.

Execution of Strategic Approach

1. Translate the problem requirements

Let's break down what Jackie needs to do in everyday terms:

• She has 100 pills total to take
• She takes them at three specific times each day: 7 a.m., 3 p.m., and 11 p.m.
• This means she takes 3 pills per day
• She starts on July 1 at 3 p.m. (which is her first pill)

So we need to figure out: when will she take pill number 100?

Process Skill: TRANSLATE - Converting the prescription schedule into a clear counting problem

2. Calculate total days needed

Now let's think about this step by step:

If Jackie takes 3 pills per day, and she needs 100 pills total, how many days will this take?

\(100 \div 3 = 33\text{ complete days plus }1\text{ extra pill}\)

Let me verify: \(33 \times 3 = 99\) pills, so she'll need one more pill after 33 complete days.

This means:

• After 33 complete days, she will have taken 99 pills
• The 100th pill will be the first pill of the 34th day

3. Track the progression from start date

Jackie starts at 3 p.m. on July 1. Let's count forward:

Day 1 (July 1): Takes pill #1 at 3 p.m., then pill #2 at 11 p.m.

Day 2 (July 2): Takes pill #3 at 7 a.m., pill #4 at 3 p.m., pill #5 at 11 p.m.

From Day 2 onward, she takes exactly 3 pills per day.

So after Day 1, she has taken 2 pills. She needs 98 more pills.

\(98 \div 3 = 32\text{ complete days plus }2\text{ extra pills}\)

This means:

• 32 complete days after July 2 takes us to August 2
• July 2 + 32 days = August 3
• On August 3, she'll take the 99th pill at 7 a.m. and the 100th pill at 3 p.m.

4. Identify the specific timing of the last pill

Let's double-check our counting:

July 1: Pill #1 (3 p.m.), Pill #2 (11 p.m.) = 2 pills total

July 2 through August 2: This is \(32 \times 3 = 96\) pills

Running total: \(2 + 96 = 98\) pills

August 3: Pill #99 (7 a.m.), Pill #100 (3 p.m.)

Therefore, Jackie should take her last pill on August 3 at 3 p.m.

Process Skill: CONSIDER ALL CASES - Carefully tracking the partial first day to avoid off-by-one errors

Final Answer

The 100th and final pill should be taken on August 3 at 3 p.m.

This matches answer choice E. August 3 at 3 p.m.

Common Faltering Points

Errors while devising the approach

1. Misunderstanding the pill-taking schedule
Students may incorrectly assume Jackie takes pills every 8 hours starting from 3 p.m. on July 1, rather than understanding she follows a fixed daily schedule of 7 a.m., 3 p.m., and 11 p.m. This leads them to calculate based on 8-hour intervals (like 3 p.m., 11 p.m., 7 a.m., 3 p.m., etc.) instead of recognizing the pattern of 3 pills per complete day.

2. Overlooking the partial first day
Many students assume Jackie starts a complete day cycle on July 1, missing that she only takes 2 pills on July 1 (at 3 p.m. and 11 p.m.) rather than the full 3 pills. This causes them to incorrectly divide 100 by 3 and add the result directly to July 1.

Errors while executing the approach

1. Incorrect date counting
Students often make errors when counting days across month boundaries. For example, they might incorrectly calculate that 32 days after July 2 leads to August 2 instead of August 3, or forget that July has 31 days when crossing from July to August.

2. Off-by-one errors in pill counting
When tracking which pill number corresponds to which day and time, students frequently miscount by one position. They might conclude the 100th pill is taken at 7 a.m. on August 3 (which would actually be the 99th pill) instead of correctly identifying it as the 3 p.m. dose on August 3.

Errors while selecting the answer

1. Selecting the second-to-last pill timing
After calculating correctly that the final day is August 3, students might select August 3 at 7 a.m. (answer choice D) thinking this is the last pill, when it's actually the 99th pill. The 100th pill comes at 3 p.m. on the same day.