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# A mixture of 16% disinfectant solution is to be made from 14% and 22% disinfectant solutions. How much of each solution should be used if 16 gallons of the 16% solution are needed? There needs to be gallons of 14% solution and gallons of 22%.

Question:

A mixture of 16% disinfectant solution is to be made from 14% and 22% disinfectant solutions. How much of each solution should be used if 16 gallons of the 16% solution are needed?

There needs to be gallons of 14% solution and gallons of 22%.

Answers (0)
• April 13, 2023 в 23:10
Let x be the number of gallons of 14% disinfectant solution needed and y be the number of gallons of 22% disinfectant solution needed. We can set up two equations based on the information given: Equation 1: x + y = 16 (since 16 gallons of the 16% solution are needed) Equation 2: 0.14x + 0.22y = 0.16(16) (since the 16% solution is a mixture of the 14% and 22% solutions) Simplifying equation 2: 0.14x + 0.22y = 2.56 Multiplying each term by 100 to eliminate decimals: 14x + 22y = 256 Now we can use substitution or elimination to solve for x and y. Let's use substitution: From equation 1, we can solve for x in terms of y: x = 16 - y Substitute this into equation 2: 14(16 - y) + 22y = 256 224 - 14y + 22y = 256 8y = 32 y = 4 Now we can solve for x using x = 16 - y: x = 16 - 4 = 12 Therefore, 12 gallons of the 14% disinfectant solution and 4 gallons of the 22% disinfectant solution should be used to make 16 gallons of the 16% disinfectant solution.
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