# More to less quantity

1. Nov 29, 2016

### zak100

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
Unitary method I think so but situation is different

3. The attempt at a solution
10 patients------ 14 days
1 patient = 14/10
35 patient = 14/10 * 35

Zulfi.

2. Nov 29, 2016

### haruspex

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?

3. Nov 29, 2016

### Staff: Mentor

How long would the same number of pills last for one patient?

4. Nov 29, 2016

### zak100

Hi,
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.

5. Nov 29, 2016

### zak100

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.

6. Nov 29, 2016

### haruspex

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?

7. Nov 29, 2016

### 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.

8. Nov 29, 2016

### 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 ?

9. Nov 30, 2016

### 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.

10. Nov 30, 2016

### Buffu

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

Similarly, x = ?

Last edited: Nov 30, 2016
11. Nov 30, 2016

### 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 dont know y. y may be: total pills/total patients.

Zulfi.

12. Nov 30, 2016

### haruspex

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

13. Nov 30, 2016

### Buffu

Yes.

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.

14. Nov 30, 2016

### 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.

15. Nov 30, 2016

### haruspex

Let's go back to here:
Call that 140 doses, i.e. one dose lasts one patient one day.
With 35 patients, how long will 140 doses last?

16. Nov 30, 2016

### Buffu

• Member warned that providing complete solutions is not permitted here
ok I will provide the complete solution.

from
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.

17. Nov 30, 2016

### 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 cant 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.

18. Nov 30, 2016

### 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.

19. Nov 30, 2016

### Buffu

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.