Math question?

Question

50 mg of an antibiotic to be given every 6 hours. Your child weighs 32 lb. Your research indicates that approximately 30 mg/kg/day is the recommended dosage.
Is this prescription safe for your child? (Show mathematically if it is safe)

If not is there an over dose or an under dose prescribed? By how much?


If not what would a safe dose be? Show your calculations to determine the safe dose.
15 ml of Tylenol3 to be given every 4 – 6 hours. Your research indicates that there are 12 mg codeine per 5 ml of liquid and that the safe dosage is approximately .75 mg/kg/dose every 4 – 6 hours.
Is this prescription safe for your child? (Show mathematically if it is safe for your child)

If not what would a safe dose be? Show your calculation to determine the safe dose for your child.

Answer 1

Antibiotic question

 

Step 1:  Convert the weight in lbs to kg  1 kg = 2.2 lbs

 

30/2.2 = 13.6 kg

 

Step 2: We multiple the weight by 30 mg to get the recommended daily dosage:  13.6(30) = 409mg/day

 

Step 3: The child is receiving 50 mg every 6 hours, which means 4 times a day.  50 mg x 4 = 200 mg. 

 

The child would be underdose by approximately 200 mg.

 

Tylenol problem: Assuming this is for the same 30 lb child

 

13.6 kg (0.75mg) = 10.2 mg of codeine/dose

 

Now we need to figure out how many mg of codeine are contained in 15 ml of TC #3 if the concentration is 12mg/5ml

 

12mg = x mg

____     _____

5 ml       15 ml

 

12(15) = 5x

180 = 5x

180/5 = x

x = 36 mg/dose

 

The child would be overdosed about 3 times if the recommended dosage about 10 mg every 4-6 hours, as 15 ml of TC#3 delivers about 36 mg per dose.

 

 

Answer 2

I'll help with the first part. Let's determine amount that is good for a day

recommended dosage is given as 

30 mg/(kg*day) 

there is 24 hours in a day

[30 mg/(kg*day)]*(1 day/24 hours)

there are 2.2 pounds per kg I believe ( might want to double check me)

so 

[30 mg/(kg*day)]*(1 day/24 hours)*(1 kg/2.2 lbs)

 

your child weighs 32 lbs so 

[30 mg/(kg*day)]*(1 day/24 hours)*(1 kg/2.2 lbs)*32 pounds

do the math and this is the recommended dosAge.

 

if doctor recommended 50 mg every 6 hours then that is 200 mg per day (50*4)

compare the numbers.

 

best - hope helpful