Lesson 3 · from § of the 1910 text
Mixture Problems
Mixture problems
In a mixture problem the unknown is usually a quantity of one ingredient to be added, or the strength of one of the parts. The equation says that the amount of the pure substance is the same whether it is counted part by part or in the whole mixture.
Example (the hint to Exercise 18). Gun metal of a certain grade is composed of 16\% tin and 84\% copper. How much tin must be added to 410 pounds of this gun metal to make a composition 18\% tin?
Since the composition is 16\% tin, \frac{16}{100} \cdot 410 = the number of pounds of tin in the first composition. Let x = the number of pounds of tin to be added. Then \frac{16 \cdot 410}{100} + x = the number of pounds of tin in the second composition, and 410 + x = the number of pounds of both metals in the second composition.
\text{Therefore}\qquad \frac{\dfrac{16 \cdot 410}{100} + x}{410 + x} = \frac{18}{100}.
When two strengths are unknown, as in Exercise 22, use two letters and two equations.
Exercises
How to type math
Use ^ for powers (a^2), / for fractions ((a+b)/2), sqrt(x) for square roots, and cbrt(x) for cube roots. You can leave out the multiplication sign: 3ab means 3 \cdot a \cdot b. Mixed numbers like 4 1/2 work too. The preview under each box shows how your answer was read.
How many ounces of alloy must be added to 56 ounces of silver to make a composition 70\% silver?
Gun metal of a certain grade is composed of 16\% tin and 84\% copper. How much tin must be added to 410 pounds of this gun metal to make a composition 18\% tin?
A 30-gallon mixture of milk and water tests 16\% cream. How much water has been added if the milk is known to test 20\% cream?
How many gallons of alcohol 90\% pure must be mixed with 10 gallons of alcohol 95\% pure so as to make a mixture 92\% pure?
It is desired to have a 10-gallon mixture of 45\% alcohol. Two mixtures, one of 95\% alcohol and another of 15\% alcohol, are to be used. How many gallons of each will be required to make the desired mixture?
A chemist has the same acid in two strengths. Eight liters of one mixed with 12 liters of the other gives a mixture 84\% pure, and 3 liters of the first mixed with 2 liters of the second gives a mixture 86\% pure. Find the per cent of purity of each acid.