word problem with combined operations

Question

A patient receives declining dosages of prednisone over a 12 day period.

 

Days given   dosage         Times per day

Days 1-3      0.01grams           three

Days 4-5       0.005                   three

Days 6-7       0.005                   twice

Days 8-9      0.0025                 twice

Days 10-12  0.00125              three

 

A. What is the decrease in total daily dosage between day 1 and day 12?

 

B. What is the total dosage given to the patient in the 12-day period? 

Answer 1

Hi Lynn,

 

This problem only involves addition, subtraction, multiplication, and an understanding of decimals, but like many word problems, the language can be a little confusing.  So let's proceed part by part:

 

A.  This question asks about the total decrease in daily dosage between days one and twelve, so we don't need to worry about the total dosage over multiple days.  That means we first figure out the total dosage for each day by multiplying the number of doses by the dosage per dose:

 

1)  3(.01) = .03; 3(.00125) = (.00375)

 

2)  Now, we simply subtract the day twelve total dosage from the day one total dosage:  .03 grams - .00375 grams = decrease in dosage.

 

2.  To complete this operation (without a calculator), add zeroes after the "3" in the hundredths place in the day one dosage, so .03000 - .00375.  Can you see that this is the same as 3000 - 375, just with different placement of the decimal? The decimal only matters for the answer.

 

3.  .03000 - .00375 = .02625

 

That takes care of A! Now, on to B, which is a little more complicated, but not much:

 

B.  What is the total dosage given to the patient in the 12-day period?  

 

1.  To get the total dosage over the whole course of treatment, the firs thing we need to do is figure out the total dosage for each day.  We already know the total dosage, from A, for days 1 - 3 and days 10 - 12:  days 1 - 3: .03 grams; days 10 - 12 = .00375.  

 

2. Now we need to find out the dosages for days 4 - 5, 6 - 7, and 8 -9, again using multiplication:  days 4 - 5 = 3(.005) = .0150; days 6 - 7 = 2(.005) = .01; days 8 - 9 = 2(.0025) = .005

 

3.  Finally, we add up the total dosages for each day.  Again, this is easier if we first multiply the total daily dosage by the number of days it applies:

 

4)  3(.03) + 2(.0150) +  2(.005) + 2(.005) + 3(.00375) = total dosage

 

5)  .09 + .03 + .01 + .0125 = total dosage.  

 

6)  .1425 grams  = total dosage

 

Done!

 

 

 

total we need to add the dosage of each day.  WE can use multiplication to simplify this task, because on some days the dosage is the same, so:

 

2.  3(.01) + 2(.005) + 2(.005)