Question

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

Answer 1

lets call the number of ounces of 5% solution \(x\) so the ounces of 2% solution must be \(1-x\) (since the total is one once)

Answer 2

damn that was wrong, it is 1% solution let me start again
lets call the number of ounces of 5% solution \(x\)so the ounces of 1% solution must be \(1−x\) (since the total is one once)

Answer 3

hmm i have .05x + .01y = 1

Answer 4

then you have \(.05x+.01(1-x)\) as the amount of hydrocortisone, and this has to be 2% of one ounce with is \(0.02\)

Answer 5

your job is to solve
\[.05x+.01(1-x)=.02\] or to make it easier multiply by 100 to clear the annoying decimals and solve
\[5x+(1-x)=2\]

Answer 6

you get \(4x+1=2\) and this is easy to solve

Answer 7

How many ounces of each?

Answer 8

isnt that only one answer?

Answer 9

what did you get for \(x\) ?

Answer 10

x= 1/4 or .25

Answer 11

right, and of course we have remember what \(x\) represents, which is why it is good to define your variable at the beginning.
first like i wrote was "lets call the number of ounces of 5% solution \(x"\)

Answer 12

so we can remember what \(x\) is supposed to be, the number of ounces of 5% solution, which turns out to be 0.25 ounces

Answer 13

then plug that in to the origional equation?

Answer 14

now that you know the amount of 5% solution, you also know the amount of 1% solution

Answer 15

since the total is one ounce

Answer 16

so .25 percent of 5 % solution and .75 of 1 %?

Answer 17

yes

Answer 18

ok thanks!

Answer 19

yw, hope method was clear