A doctor prescribes an ointment that is 2% hydrocortisone. A pharmacist has 1% and 5% concentrations in stock. How many ounces of each should the pharmacist use to make a 9-ounce tube?

Question

anonymous · Answer

you want 9 ounches of 2%. so the total amount of 1% and 5% lotion has to be total to 9. 

if you add 2ounches of the 1% to 2ounches of the 5% you would get 4 ounches of 3% (the mean value of the two since you add it in equal ammounts.
now if you would only do 1 ounch of the 5% and 2 of the 1% you would do: (2* 1 + 1 * 5)/3 =2.3333 percent and a 3 ounch lotion. try to find the values that give you 2% then convert it to 9 ounches

anonymous · Answer

Let x ounces of 1% and (9-x) of 5% of hydrocortisone be be mixed to form 9 ounces of 2% hydrocortisone.
$$x*\frac{ 1 }{100 }+(9-x)*\frac{ 5 }{100 }=9*\frac{ 2 }{100 }$$
orx+5(9-x)=18
solve for x ,you get the solution.

anonymous · Answer

so I come up with 6.75 oz is that right?

anonymous · Answer

yes

anonymous · Answer

but which concentration does it go to the 5% or the one%

anonymous · Answer

it goes to 1%
as i have mentioned x ounces of 1%

anonymous · Answer

thanks that helps out a lot!

anonymous · Answer

yw