A pharmacist is to prepare a 50 fluid ounce solution that contains 54% glucose. The pharmacy has a 30% solution and a 90% solution on hand. How many ounces of each solution should be mixed to prepare the desired perscription?
.3x + .9(50-x) = .54(50)
Solve for x
Can you see what the equation says?
Ya it says How many ounces of each solution should be mixed to prepare the desired perscription? Why is there a 50 in parentheses next to the .54? So once I solve for x what do I do next?
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To solve this problem, we can set up a system of equations based on the given information. Let's assume x represents the number of ounces of the 30% solution and y represents the number of ounces of the 90% solution.
We know that the total volume of the solution is 50 fluid ounces. Therefore, the first equation is:
x + y = 50
We also know that the desired solution should be 54% glucose. This means that the amount of glucose in the 30% solution plus the amount of glucose in the 90% solution should equal 54% of the total volume of the mixture.
The amount of glucose in the 30% solution is 0.30x (as the solution is 30% glucose), and the amount of glucose in the 90% solution is 0.90y (as the solution is 90% glucose). Therefore, our second equation is:
0.30x + 0.90y = 0.54 * 50
Now we have a system of two equations:
x + y = 50 (equation 1)
0.30x + 0.90y = 0.54 * 50 (equation 2)
To solve this system, we can use substitution, elimination, or graphing methods. Let's solve it using the substitution method:
From equation 1, we can rearrange it to express x in terms of y:
x = 50 - y
Substitute this expression for x into equation 2:
0.30(50-y) + 0.90y = 0.54 * 50
Simplify the equation:
15 - 0.30y + 0.90y = 27
Combine like terms:
0.60y = 12
Divide both sides by 0.60:
y = 20
Now substitute this value for y back into equation 1 to find x:
x + 20 = 50
x = 30
Therefore, you need 30 ounces of the 30% solution and 20 ounces of the 90% solution to prepare the desired prescription.