A mixture of 17 %disinfectant solution is to be made from 10% and 20% disinfectant solution. How much of each solution should be used if 20 gallons of the 17% solution are needed?

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Teagan

Mathematics

5 January, 15:41

A mixture of 17 %disinfectant solution is to be made from 10% and 20% disinfectant solution. How much of each solution should be used if 20 gallons of the 17% solution are needed?

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Jazmyn Sullivan · Answer 1

Since 20 total gallons are needed, the amount of 10% solutions can be x and the amount of 20% solutions can be (20-x) since they add up to 20. In addition, the 17% solution has 20 gallons. Putting this into an equation, we get that 10% is 0.1 (by moving the decimal 2 spots to the left), 0.2=20%, and 0.17=17%. With that information, we can determine that 10%*x+20% * (20-x) = 20*0.17 due to that with 20 gallons of the 27% solution, we need a certain amount of solution. For every gallon, we add 0.17 of the solution, so we have 20*0.17. Similarly, we want that total amount to be represented by the amount of 20% + the amount of 10%.

0.1x+0.2 (20-x) = 0.1x+4-0.2x=-0.1x+4 using the distributive property

-0.1x+4=20*0.17=3.4. Subtract 4 from both sides to get - 0.1x=-0.6, and multiply both sides by - 10 (to separate x) to get x=6. Therefore, the amount of 10% solution is 6 gallons and the amount of 20% solution is 20-5=14 gallons