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?

Given,

Solution A contains 2 parts salt to 8 parts water

Solution B contains 3 parts salt to 5 parts water

Target Mixture contains3 parts salt to 7 parts water:

Expressing the salt concentration in decimal form
Solution A: 2/(2 + 8) = 2/10 = 0.20 salt

Solution B: 3/(3 + 5) = 3/8 = 0.375 salt

Mixed Solution: s/(3 + 7) = 3/10 = 0.30 salt

Since target mixture is 280 quarts
If the amount of 0.375 salt present in mixed solution = x

Then, the amount of 0.20 salt, y = 280 – x

Using a typical mixture equation
0.375x + 0.20(280-x) = 0.30(280)
0.375x + 56 - 0.20x = 84

Subtract 56 from both sides of the equation
0.375x - 0.20x + 56 – 56 = 84 – 56

0.375x - 0.20x = 28
0.175x = 28

Divide both sides of the equation by 0.175

0.175x/0.175 = 28/0.175
x = 160

y = 280 – x

y = 280 – 160

y = 120

Therefore,

x = 160 quarts of the solution that contains 3 parts salt to 5 parts water

y = 120 quarts of the solution that contains 2 parts salt to 8 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 one solution contains 2 parts salt to 8 parts water.

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

Step 2:

The another solution contains 3 parts salt to 5 parts water.

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

Step 3:

It is given that the volume of the final mixture is 280 quartz of a solution in which 3 parts salt to 7 parts water.

Therefore, the salt concentration in the final solution can be expressed in decimal form 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 is 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 calculated 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