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A doctor prescribes an ointment that is 4% hydrocortisone. A pharmacist has 1% and 5% concentrations in stock. How many ounces of each should the pharmacist use to make a 5-ounce tube?.

Respuesta :

Answer:

[tex]1.25[/tex] ounes of [tex]1[/tex]% and [tex]3.75[/tex] ounes of [tex]5[/tex]% will be used to make a [tex]5[/tex]-ounce tube

Explanation:

let "x" represent the number of ounces of  [tex]1[/tex]% concentration

Then the number of ounces of  [tex]5[/tex]%concentration would be [tex]5-x[/tex]

Now the total of ounces of  [tex]1[/tex]% and  [tex]5[/tex]% would be equal to [tex]5[/tex]-ounce of [tex]4[/tex]% hydrocortisone.

so the equation will be

[tex]0.01 (x) + 0.05(5-x) = 0.04*5\\0.01x-0.05x+0.25= 0.2\\\\0.25-0.2= 0.04x\\x = \frac{0.05}{0.04} \\x= 1.25\\5-x= 5-1.25 = 3.75[/tex]

hence

[tex]1.25[/tex] ounes of [tex]1[/tex]% and [tex]3.75[/tex] ounes of [tex]5[/tex]% will be used to make a [tex]5[/tex]-ounce tube

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