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Chapter 11: Q. 67 (page 715)

A doctor鈥檚 prescription calls for a daily intake containing 40 milligrams (mg) of vitamin C and 30 mg of vitamin D. Your pharmacy stocks two liquids that can be used: one contains 20% vitamin C and 30% vitamin D, the other 40% vitamin C and 20% vitamin D. How many milligrams of each compound should be mixed to fill the prescription?

Short Answer

Expert verified

It is necessary to mix 75mg of the first compound and 50 mg of the second compound

Step by step solution

01

Given information

Your pharmacy stocks two liquids that can

be used: one contains 20% vitamin C and 30% vitamin D, the other 40% vitamin C and 20% vitamin D.

02

Find the equations

Let x be the first liquid and y be the second liquid

We are given

Your pharmacy stocks two liquids that can

be used: one contains 20% vitamin C and 30% vitamin D,

Hence

0.2x+0.4y=402x+4y=400(1)

The other 40% vitamin C and 20% vitamin D.

Hence we get,

0.3x+0.2y=303x+2y=300(2)

03

Solve the equation

To solve the equation

Multiply equation 2 by 2 and subtract it from 1

We get,

2x+4y=400-6x-4y=-600-4x=-200

Therefore we get,

x=50

Also we find the value of y

2x+4y=4002(50)+4y=4004y=300y=75

04

Conclusion

It is necessary to mix 75mg of the first compound and 50 mg of the second compound

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