# Calculating Pill Quantity for Patient Treatment: 10 vs. 35 - Find the Duration

• zak100
In summary, the hospital has enough pills to treat 10 patients for 14 days, but the same number of pills would only last one patient for 140 days. Therefore, with 35 patients, the pills will last for 4 days. The key to solving this problem is to understand the relationship between the number of pills, number of patients, and number of days they will last. By setting up equations for different scenarios, you can find the solution for any given number of patients.
zak100

## Homework Statement

A hospital has enough pills on hand to treat 10 patients for 14 days. How long will the pills last if there are 35 patients?

## Homework Equations

Unitary method I think so but situation is different

## The Attempt at a Solution

10 patients------ 14 days
1 patient = 14/10
35 patient = 14/10 * 35

Zulfi.

zak100 said:
1 patient = 14/10
Think about it, does that make sense? That there are enough pills to supply 10 patients for two weeks, but that's not enough to keep one patient going for two days?

zak100 said:
A hospital has enough pills on hand to treat 10 patients for 14 days.
How long would the same number of pills last for one patient?

Hi,
Think about it, does that make sense? That there are enough pills to supply 10 patients for two weeks, but that's not enough to keep one patient going for two days?
How you got two days?
14/10 =1.4
Okay one patient out of those 10 will also get the pills for 2 weeks.
Whats the next step?
Zulfi.

Hi,
Mark44 said:
How long would the same number of pills last for one patient?
For 14 days, if he is from same 10 patient group and not a new one.
Plz guide me what is the next step.

Zulfi.

zak100 said:
Hi,

For 14 days, if he is from same 10 patient group and not a new one.
Plz guide me what is the next step.

Zulfi.
Maybe you have not understood the question.
The hospital has some number of pills.
If 10 patients require a course of these pills then that number of pills will last for 14 days.
If, instead, there were only one patient, how many days would that number of pills last?

Hi,
Thanks for giving me special attention.
If there is only one patient then it would last for 14 * 10 days.
Plz guide me the next step. Thanks for your time.

Zulfi.

let the total pills be x.
let pills used by one patient be y per day.

What is x in terms of y ?

let the number of days pills lasted when the number of patients is 35 be z.

What is z in terms of x and y ?

Hi,
I have tried.
x= total pills= not given in the question
y= pills by one patient/day= x/14=
x= 14 * y
z= # of days pills lasted when patient is 35? (actually this is the question)
z=14 * y/35
How to find y?
Zulfi.

zak100 said:
x= 14 * y
No,
x is total pill and y is pills per patient per day,
x = (number of patient)*(number of days)*y
So x = ?

zak100 said:
z=14 * y/35
Similarly, x = ?

Last edited:
Hi,
<<x = (number of patient)(number of days)y>>
In the above equation its unclear whether you are dividing by y or multiplying by y
x= 10 * 14 * y
Is the above correct?
What is y? y= Number of pills per day
I don't know y. y may be: total pills/total patients.

Zulfi.

Buffu said:
let pills used by one patient be y per day
That's an unnecessary complication. Just deal in daily doses.

Buffu
zak100 said:
x= 10 * 14 * y
Is the above correct?

Yes.

zak100 said:
What is y? y= Number of pills per day
I don't know y. y may be: total pills/total patients.

y is the daily dose of one patient.
____________________________________________
Now all you need is to find z in terms of x and y, then evaluate z.

Hi,
Thanks every body who is helping me.
y = total days /total patients=14/10
x= 10 * 14 * y = 10 * 14 * 14/10
Is the above correct
Zulfi.

Let's go back to here:
zak100 said:
If there is only one patient then it would last for 14 * 10 days
Call that 140 doses, i.e. one dose lasts one patient one day.
With 35 patients, how long will 140 doses last?

Member warned that providing complete solutions is not permitted here
zak100 said:
Hi,
Thanks every body who is helping me.
y = total days /total patients=14/10
x= 10 * 14 * y = 10 * 14 * 14/10
Is the above correct
Zulfi.

ok I will provide the complete solution.

from
zak100 said:
<<x = (number of patient)(number of days)y>>
In the above equation its unclear whether you are dividing by y or multiplying by y
x= 10 * 14 * y
we get x = 14 * 10 * y ----- (1)
_________________________________________
Now number of patient is given as 35 and number of days is what we need to find. So,
x = (number of patient)(number of days)y
Or,
x= 35 * z *y ---- (2)

Dividing (1) by (2)
we get,

$${x\over x} = {10 * 14 * y\over 35 * z* y}$$
$$\implies 1 = {140\over 35z}$$
$$\implies z = 4$$

We are done.

Hi thanks my friend. Good work. I appreciate it. Actually i was not worried about the solution. Solution was already present in the book. I want to know the method of solving these problems. These can't be solved by unity method. So how to solve it.
You have shown me to find out two eq for the same variable using different values of patients, total number of days pills would last and the number of pills taken/ day.
x was unknown. x = total pills= total days they would last (14 first time & named as z for second x) * total patients * pills taken per day.

Okay i would apply this technique in other questions.

Zulfi.

Hi haruspex,
Thanks.
<<Call that 140 doses, i.e. one dose lasts one patient one day. With 35 patients, how long will 140 doses last?>>

140/35=4 days.

Okay i would try another question & check which method is easy.
Zulfi.

zak100 said:
Hi thanks my friend. Good work. I appreciate it. Actually i was not worried about the solution. Solution was already present in the book. I want to know the method of solving these problems. These can't be solved by unity method. So how to solve it.
You have shown me to find out two eq for the same variable using different values of patients, total number of days pills would last and the number of pills taken/ day.
x was unknown. x = total pills= total days they would last (14 first time & named as z for second x) * total patients * pills taken per day.

Okay i would apply this technique in other questions.

Zulfi.

I am very bad at solving these types of problems but what I do is to make a variable for every possible thing and then solve for what is asked. You probably just a bit of practice and you will master these type of problems.

## 1. How do I calculate the pill quantity for a patient's treatment?

The pill quantity for a patient's treatment can be calculated by dividing the total number of pills needed for the entire treatment duration by the number of pills that the patient needs to take per day. This will give you the total number of days the treatment will last, and from there you can determine the amount of pills needed for each prescription refill.

## 2. What factors should be considered when calculating the pill quantity for a patient's treatment?

Some factors to consider when calculating the pill quantity for a patient's treatment include the patient's dosage, frequency of dosage, and the total duration of the treatment. It is also important to take into account any potential changes in dosage or treatment plan that may occur during the course of the treatment.

## 3. How does the dosage and frequency affect the amount of pills needed for a patient's treatment?

The dosage and frequency of a patient's treatment will directly impact the amount of pills needed. A higher dosage or more frequent dosing will require a larger pill quantity, while a lower dosage or less frequent dosing will require a smaller pill quantity. It is important to carefully follow the prescribed dosage and frequency to ensure the correct amount of pills are taken for the treatment.

## 4. Is there a difference in calculating the pill quantity for a treatment that lasts 10 days versus 35 days?

Yes, there can be a difference in calculating the pill quantity for different treatment durations. For a treatment that lasts 10 days, the pill quantity will be smaller compared to a treatment that lasts 35 days. This is because the total number of pills needed for a longer treatment duration will be higher, and the number of pills needed per day will also be higher.

## 5. How can I ensure accuracy when calculating the pill quantity for a patient's treatment?

To ensure accuracy when calculating the pill quantity for a patient's treatment, it is important to double check your calculations and take into account any potential changes in dosage or treatment plan. It may also be helpful to consult with a medical professional for guidance and to review the calculations. Additionally, using a calculator or spreadsheet can help minimize errors in the calculation process.

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