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

[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
which is giving a wrong answer. Somebody please guide me.

Zulfi.

 

[haruspex]

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?

 

[Mark44]

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?

 

[zak100]

Hi,
Thanks for your reply.

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.

 

[zak100]

Hi,
Thanks for your reply.

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.

 

[haruspex]

Hi,
Thanks for your reply.

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?

 

[zak100]

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.

 

[Buffu]

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 ?

 

[zak100]

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.

 

[Buffu]

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 = ?

z=14 * y/35

Similarly, x = ?

 

[zak100]

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.

 

[haruspex]

let pills used by one patient be y per day

That's an unnecessary complication. Just deal in daily doses.

 

[Buffu]

x= 10 * 14 * y
Is the above correct?

Yes.

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.

 

[zak100]

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.

 

[haruspex]

Let's go back to here:

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?

 

[Buffu]

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

<<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.

 

[zak100]

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.

 

[zak100]

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.

 

[Buffu]

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.