Medication Dosage Problem: Total Tablets Required

Medication Dosage 7th-8th Grade
PROBLEM
Drug C is available in 5 mg tablets. A patient needs 25 mg daily for 7 days, then 15 mg daily for 7 days, then 5 mg daily for 7 days. How many tablets will the patient require in total?

What This Problem Teaches

  • Converting between medication doses (mg) and number of tablets based on tablet strength
  • Breaking complex multi-phase problems into manageable pieces
  • Understanding medication tapering schedules and their practical implementation
  • Unit conversion skills critical for healthcare professionals
  • Systematic calculation methods to prevent potentially dangerous dosing errors
Drug C is available in 5 mg tablets. A patient needs 25 mg daily for 7 days, then 15 mg daily for 7 days, then 5 mg...

Solution: Method 1 — Phase-by-Phase Calculation

The most reliable approach for medication dosage problems is to calculate tablets needed for each phase separately, then add them together. This method minimizes errors and matches how pharmacists actually dispense medications.

Step 1 — Calculate tablets needed for Week 1 (25 mg daily)

First, determine how many tablets are needed per day in the first phase:

Tablets per day = Daily dose ÷ Tablet strength
Tablets per day = 25 mg ÷ 5 mg per tablet = 5 tablets per day

Then multiply by the number of days in this phase:

Week 1 total = 5 tablets/day × 7 days = 35 tablets

Step 2 — Calculate tablets needed for Week 2 (15 mg daily)

Repeat the process for the second phase:

Tablets per day = 15 mg ÷ 5 mg per tablet = 3 tablets per day
Week 2 total = 3 tablets/day × 7 days = 21 tablets

Step 3 — Calculate tablets needed for Week 3 (5 mg daily)

And for the final phase:

Tablets per day = 5 mg ÷ 5 mg per tablet = 1 tablet per day
Week 3 total = 1 tablet/day × 7 days = 7 tablets

Step 4 — Add all phases together

Sum the tablets from all three phases:

Total tablets = 35 + 21 + 7 = 63 tablets

Solution: Method 2 — Total Milligrams First

An alternative approach calculates the total milligrams needed across all phases, then converts that total to tablets. This method can be faster but requires more careful attention to avoid arithmetic errors.

Step 1 — Calculate total milligrams for each phase

Week 1: 25 mg/day × 7 days = 175 mg
Week 2: 15 mg/day × 7 days = 105 mg
Week 3: 5 mg/day × 7 days = 35 mg

Step 2 — Add up total milligrams needed

Total mg = 175 + 105 + 35 = 315 mg

Step 3 — Convert total milligrams to tablets

Total tablets = 315 mg ÷ 5 mg per tablet = 63 tablets
The patient will require 63 tablets for the complete 21-day treatment course.

Verification

Let's verify our answer using both methods to ensure accuracy:

Check using Method 1:

Week 1: 5 tablets/day × 7 days = 35 tablets ✓
Week 2: 3 tablets/day × 7 days = 21 tablets ✓
Week 3: 1 tablet/day × 7 days = 7 tablets ✓
Total: 35 + 21 + 7 = 63 tablets ✓

Cross-check using Method 2:

Total mg needed: (25×7) + (15×7) + (5×7) = 175 + 105 + 35 = 315 mg
Total tablets: 315 mg ÷ 5 mg/tablet = 63 tablets ✓

Both methods give the same answer, confirming our calculation is correct.

Common Pitfalls in Dosage Calculations

✗ Mistake 1: Forgetting to multiply by the number of days

Calculating 25 ÷ 5 = 5 and stopping there, forgetting that this is tablets per day, not total tablets. The correct calculation is 5 tablets/day × 7 days = 35 tablets for Week 1 alone.

✗ Mistake 2: Using the wrong tablet strength

Confusing the required dose with the tablet strength. Each tablet contains 5 mg, not 25 mg. So for the 25 mg dose, you need 25 ÷ 5 = 5 tablets, not 1 tablet.

✗ Mistake 3: Adding doses instead of tablets

Incorrectly adding 25 + 15 + 5 = 45 and thinking this is the answer. These are daily doses in mg, not tablet counts. Each phase must be calculated separately and then the tablet counts are added.

Clinical Safety Note: In healthcare settings, dosage calculation errors can have serious consequences. Always double-check calculations using a different method, and never skip the verification step.

Understanding Medication Tapers

This problem demonstrates a typical medication taper schedule. Tapering involves gradually reducing doses over time rather than stopping abruptly, which helps:

  • Minimize withdrawal symptoms
  • Allow the body to adjust to lower medication levels
  • Reduce the risk of rebound effects
  • Provide a safer discontinuation pathway

The pattern here (25 mg → 15 mg → 5 mg) represents decreases of 10 mg every week, following a linear reduction schedule that's common for many medications.

How to Spot This Problem Type

Medication dosage problems are easily recognizable by these key features:

  • "Available in [X] mg tablets" — signals you need to convert doses to tablet counts
  • Multi-phase schedules — different doses for different time periods
  • "Daily for [X] days" — indicates you need to multiply by duration
  • "Total tablets needed" — confirms you're calculating across the entire regimen
  • Tapering language — "then," "followed by," or decreasing dose amounts

These problems frequently appear on nursing exams (NCLEX), pharmacy calculations, and healthcare certification tests. The calculation structure is always the same: convert dose to tablets per day, multiply by days, sum across phases.

Why This Matters in Healthcare

Accurate tablet calculations are fundamental to patient safety:

In Nursing Practice: Nurses must verify that patients receive exactly the prescribed dose. Over-dispensing wastes medication and may cause toxicity; under-dispensing compromises treatment effectiveness.

In Pharmacy: Pharmacists must dispense the correct quantity to ensure patients can complete their full course of treatment without running out of medication prematurely.

For Patients: Understanding tablet counts helps patients budget for medication costs and ensures they request refills at appropriate times.

What If? — Practice Variations

1
Extended Taper Schedule
A patient needs 30 mg daily for 5 days, then 20 mg daily for 10 days, then 10 mg daily for 5 days. All tablets are 5 mg strength. How many tablets are needed in total?
Step 1 — Calculate Phase 1 tablets

30 mg ÷ 5 mg = 6 tablets/day × 5 days = 30 tablets

Step 2 — Calculate Phase 2 tablets

20 mg ÷ 5 mg = 4 tablets/day × 10 days = 40 tablets

Step 3 — Calculate Phase 3 tablets

10 mg ÷ 5 mg = 2 tablets/day × 5 days = 10 tablets

Step 4 — Sum all phases

30 + 40 + 10 = 80 tablets

Verification

Total mg: (30×5) + (20×10) + (10×5) = 150 + 200 + 50 = 400 mg
Total tablets: 400 mg ÷ 5 mg/tablet = 80 tablets ✓

Answer: 80 tablets

2
Reverse Calculation
A patient has exactly 84 tablets (5 mg each). The prescription is: take X mg daily for 7 days, then (X-10) mg daily for 7 days, then (X-20) mg daily for 7 days, using all tablets. Find the starting daily dose X.
Step 1 — Set up the equation

Total tablets = tablets from all three phases
84 = (X÷5)×7 + ((X-10)÷5)×7 + ((X-20)÷5)×7

Step 2 — Simplify by factoring out 7÷5

84 = (7÷5) × [X + (X-10) + (X-20)]
84 = (7÷5) × [3X - 30]
84 = (7/5) × (3X - 30)

Step 3 — Solve for X

84 × (5/7) = 3X - 30
60 = 3X - 30
90 = 3X
X = 30

Verification

Week 1: 30 mg ÷ 5 × 7 = 42 tablets
Week 2: 20 mg ÷ 5 × 7 = 28 tablets
Week 3: 10 mg ÷ 5 × 7 = 14 tablets
Total: 42 + 28 + 14 = 84 tablets ✓

Answer: X = 30 mg (starting daily dose)

3
Adding a Loading Dose
The regimen now includes a single loading dose of 40 mg on Day 1 only, followed by the original schedule (25 mg/day for the next 6 days of Week 1, then 15 mg/day for 7 days, then 5 mg/day for 7 days). How many tablets are needed for the full course?
Step 1 — Calculate loading dose tablets

Loading dose: 40 mg ÷ 5 mg = 8 tablets (Day 1 only)

Step 2 — Calculate remaining Week 1 tablets

Days 2-7: 25 mg ÷ 5 mg = 5 tablets/day × 6 days = 30 tablets

Step 3 — Calculate Week 2 tablets

Week 2: 15 mg ÷ 5 mg = 3 tablets/day × 7 days = 21 tablets

Step 4 — Calculate Week 3 tablets

Week 3: 5 mg ÷ 5 mg = 1 tablet/day × 7 days = 7 tablets

Step 5 — Sum all components

Total: 8 + 30 + 21 + 7 = 66 tablets

Verification

Total mg: 40 + (25×6) + (15×7) + (5×7) = 40 + 150 + 105 + 35 = 330 mg
Total tablets: 330 ÷ 5 = 66 tablets ✓

Answer: 66 tablets

4
Mixed Tablet Strengths
The pharmacy has both 5 mg tablets AND 2.5 mg tablets available. To minimize the number of pills taken per day, find the most efficient combination for each phase of the original regimen (25mg, 15mg, 5mg daily phases), and calculate the total count of each strength needed.
Step 1 — Optimize Week 1 (25 mg/day)

25 mg = 5×5mg + 0×2.5mg = 5 tablets/day (minimum possible)
Week 1 needs: 5×5mg tablets/day × 7 days = 35×5mg tablets

Step 2 — Optimize Week 2 (15 mg/day)

15 mg = 3×5mg + 0×2.5mg = 3 tablets/day
Week 2 needs: 3×5mg tablets/day × 7 days = 21×5mg tablets

Step 3 — Optimize Week 3 (5 mg/day)

5 mg = 1×5mg + 0×2.5mg = 1 tablet/day
Week 3 needs: 1×5mg tablet/day × 7 days = 7×5mg tablets

Step 4 — Calculate totals

Total 5mg tablets: 35 + 21 + 7 = 63 tablets
Total 2.5mg tablets: 0 + 0 + 0 = 0 tablets
Total pills per day: 5, 3, 1 (respectively)

Verification

All required doses are multiples of 5mg, so using only 5mg tablets is already optimal. The 2.5mg tablets provide no advantage for minimizing daily pill count in this particular regimen.

Answer: 63 tablets of 5mg strength, 0 tablets of 2.5mg strength

Frequently Asked Questions

How do you calculate total tablets needed for a tapering medication schedule?+

Calculate tablets needed for each phase separately, then add them up. For each phase: divide the daily dose by tablet strength to get tablets per day, then multiply by the number of days. In this problem: Week 1 needs 5 tablets/day × 7 days = 35 tablets, Week 2 needs 3 tablets/day × 7 days = 21 tablets, Week 3 needs 1 tablet/day × 7 days = 7 tablets, for a total of 63 tablets.

What is a medication taper and why is it prescribed?+

A medication taper is a gradual reduction in dose over time, used to safely discontinue medications or minimize side effects. This problem shows a typical taper: starting at 25mg daily, reducing to 15mg, then to 5mg over three weeks before stopping completely.

How do you convert milligrams to number of tablets?+

Divide the required dose by the tablet strength. If you need 25mg and each tablet contains 5mg, you need 25 ÷ 5 = 5 tablets. Always check that the required dose divides evenly by the tablet strength, or determine if partial tablets are acceptable.

NJ
Neven Jurkovic, PhD

Professor of Computer Science, Palo Alto College, Alamo Colleges District, San Antonio, TX

Developer of Algebrator

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This solution was prepared with AI assistance and reviewed by Dr. Jurkovic for mathematical accuracy and pedagogical clarity.

2026-09-01