A total of 25 mg of y compound and 50 mg of x compound should be mixed to fill the prescription.
How many milligrams of each compound should be mixed to fill the prescription?
Given:
- A doctor's prescription calls for a daily intake containing 50 mg of vitamin C and 100 mg of vitamin D.
- Your pharmacy stocks two compounds that can be used: one contains 80% vitamin C and 10% vitamin D, the other 40% vitamin C and 20% vitamin D.
Find:
- How many milligrams of each compound should be mixed to fill the prescription.
Solution:
So, as per the condition given in the question, we get;
0.8x+0.4y=50
0.1x+0.2y=10
We can also write the above equation as;
8x+4y=500
x+2y=100
We can write the second equation as;
x = 100 - 2y
Now, putting the value of x in the first equation, we get;
8(100-2y)+4y=500
800-16y+4y=500
12y=300
y=25
Now,putting the value of y in x equation, we get;
x = 100 - 2y
x = 100 - 2*25
x =100 - 50
x = 50
Hence, 50 mg of x of each compound and 25 mg of y of each compound should be mixed to fill the prescription.
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