SOLUTION: a mixture of 8% disenfectants solution is to be made from 10 % and 7% diseenfectant solution. How much of ech solution should be used if 30 galllons of 8% solution are needed?

Question 443683: a mixture of 8% disenfectants solution is to be made from 10 % and 7% diseenfectant solution. How much of ech solution should be used if 30 galllons of 8% solution are needed?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
What are we told the goal is produce 30 gallons of an 8% disinfectant.
We have unlimited supplies of 10% and 7% solutions to mix together.
With most mixture problems it helps to figure out how much "pure" stuff you will have.
.08*30 = 2.4 gallons of pure stuff in the 30 gallons.
Setting up the specific equation to solve uses this information.
.
First,
x = amount of 10% solution we will use,
so
30-x = amount of 7% solution we will use.
.
Second,
x*.10 + (30-x)*.07 = 30*.08
.10x + 2.1 - .07x = 2.4
Multiply by 100 to eliminate the decimals
10x + 210 - 7x = 240
3x + 210 = 240
3x = 30
x = 10 gallons of 10% solution
30-x = 20 gallons of 7% solution
.
Always check your work!
.
In this case, we know we have 30 gallons (10+20), so we need to check how much pure stuff we have contained in the 30 gallons.
10*.10 = 1 gallon of pure stuff coming from the 10% component.
20*.07 = 1.4 gallons of pure stuff coming from the 7% component.
1 + 1.4 = 2.4 gallons of pure stuff contained in the 30 gallons, which is what we needed.
.
Answer: Use 10 gallons of 10% solution and 20 gallons to 7% solution to produce 30 gallons of 8% solution.
.
Done.
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