statistics help needed

Question

A patient has been prescribed 30 mg per day of Benadryl. The patient prefers to take liquid Benadryl which has a concentration of 12.5 mg/5 mL (12.5 mg of medication per 5 mL of liquid). Each bottle contains 118 mL of liquid. How much will the patient need to spend on liquid Benadryl in a year if it costs $5.49 per bottle? 

Hint: He can’t buy a partial bottle of medicine. Calculate the number of bottles he needs altogether BEFORE you calculate the price.

Useful conversion factor: 365 days = 1 year 

On the paper quiz, this is an extra credit question. You will not be required to use dimensional analysis if you attempt the problem, but you must document how you are paying attention to labels if you use another method. Just for extra practice, show how you would use dimensional analysis to solve this problem. 

Choose all of the fractions that are multiplied together to calculate the number of bottles only using dimensional analysis.

1 day

30 mg

1 year

365 days

365 days

1 year

5 mL

12.5 mg

30 mg

1 day

1 bottle

118 mL

12.5 mg

5 mL

118 mL

1 bottle

The quiz does not require you to write down this step, but it is necessary to find the number of bottles he needs BEFORE applying the price. 

How many bottles of Benadryl must the patient purchase to have a full year's supply? Remember that he can't buy a partial bottle. 

 bottles = ?

How much will the patient need to spend on liquid Benadryl in a year if it costs $5.49 per bottle?

$ = ?

Answer 1

Tonya,

The person requires 30mg/day x 365 days/year=10,950 mg/yr

Each bottle contains 12.5/5 mg/ml x 118ml=295 mg/botttle

The number of bottles =10950/295=37.12 which needs to be rounded up to 38 whole bottles.

The cost/year=38 bottles/yearx$/bottle=208.62 $/year

Jim