Question

The ruthless queen has asked the royal physician to come
up with a cure for laziness for her son Reginald. The
physician, not knowing what else to do, mixed 1 ounce of
a substance containing 3.7% ground cinnamon with
another substance containing 7.9% ground cinnamon to
create a substance with 6.5% ground cinnamon. How
many ounces of the 7.9% substance did he use?

Answer 1

The amount of ounces of the 7.9% substance is 2 ounces

How to determine the how many ounces of the 7.9% he used?

We know that amount m = CV where

• c = concentration and
• V = volume

Let

• m = amount of 3.7 %  ,
• m' = amount of 7.9 % and
• M = amount of 6.5 %

We have that m + m' = M

cv + c'v' = CV where

• c = 3.7 % conentration  = 0.037
• v = volume of 3.7 % = 1 ounce ,
• c = 7.9% concentration = 0.079,
• v' = volume of 7.9%,
• C = 6.5 % concentration = 0.065 and
• V = volume of 6.5% = v + v'

Since cv + c'v' = CV

Substituting the values of the variables into the equation, we have

3.7% × 1/3.7% + 7.9 %v' = 6.5%(v + v')

3.7% + 7.9 %v' = 6.5%(1 + v')

3.7% + 7.9 %v' = 6.5% + 6.5%v'

7.9%v' - 6.5%v' = 6.5% - 3.7%

1.4%v' = 2.8%

v' = 2.8%/1.4%

v' = 2 ounces

So, the amount of ounces of the 7.9% substance is 2 ounces

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