One solution contains 2 parts salt to 8 parts water, and another contains 3 parts salt to 5 parts water. how much of each should be mixed together in order to obtain 280 quarts of a solution that is 3 parts salt to 7 parts water?

The volume of the first solution and second solution is respectively.

Further explanation:  

Step by step explanation:

Step 1:

It is given that first solution has 2 parts salt to 8 parts water.

Therefore, the salt concentration in decimal form for the first solution can be expressed as,

Step 2:

The second solution has 3 parts salt to 5 parts water.

Therefore, the salt concentration in decimal form for the second solution can be expressed as,

Step 3:

The given volume of the final mixture is 280 quartz that has 3 parts salt to 7 parts water.

Therefore, the salt concentration in decimal form for the final solution can be expressed as,

Consider be the volume of the second solution in which salt present in the final solution.

Therefore, the second solution can be expressed as .

The volume of the first solution is in which salt present in the final solution.

Therefore, the first solution can be expressed as .

Step 4:

The final mixture can be written as the sum of the first solution and second solution.

The equation for final mixture can be expressed as,

Now simplify the further solution.

Therefore, the volume of the second solution is .

The volume of the first solution can be evaluated as,

Therefore, the volume of the first solution is .

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Linear equation

Keywords: mixture, solution, percent, volume, salt, water, quartz, equation, linear form, fraction, distributive property, denominator, numerator, mixed together, expression

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1