• anonymous
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 2 ounce tube?
  • Stacey Warren - Expert
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  • chestercat
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  • Nurali
Let x be the amount of the 1% concentration used. Let y be the amount of the 5% concentration used. The concentration of the two mixed will be the average amount of hydrocortisone per ounce. To find the average take (0.01x + 0.05y)/(x+y). You know that this expression needs to equal 0.04, since you're aiming for a 4% concentration. You also know that x + y must equal 2 since the pharmacist needs to make a 2 ounce tube of the ointment. This means that 0.01x + 0.05y must equal 0.04 since the denominator x + y is 1. So now you have a system of 2 linear equations: 0.01x + 0.05y = 0.04 x + y= 2 Multiply both sides of the top equation by 100 to get: x + 5y = 4 x + y = 2 Subtract the bottom equation from the top equation to get: 4y = 2 So y = 2/4=1/2 ounces and therefore x = 3/2 ounce.

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