Mathematics, 04.08.2019 14:30 clarawulf9477

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?

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Answer from: 123userhi

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

Answer from: itzia00

The volume of the first solution and second solution is $\boxed{{\mathbf{160 quartz\;, 120 quartz\;\;}}}$ 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,

$\begin{aligned}{\text{salt concentration}} &= \frac{2}{{2 + 8}} \\&= \frac{2}{{10}} \\&={\text{ 0}}{\text{.20 salt}} \\\end{aligned}$

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,

$\begin{aligned}{\text{salt concentration}} &= \frac{3}{{3 + 5}} \\&= \frac{3}{8} \\&={\text{ 0}}{\text{.375 salt}} \\\end{aligned}$

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,

$\begin{aligned}{\text{salt concentration}} &= \frac{3}{{3 + 7}} \\&= \frac{3}{{10}} \\&={\text{ 0}}{\text{.30 salt}} \\\end{aligned}$

Consider be the volume of the second solution in which 0.375 salt present in the final solution.

Therefore, the second solution can be expressed as 0.375x .

The volume of the first solution is 280 - x in which 0.20 salt present in the final solution.

Therefore, the first solution can be expressed as $\left( {280 - x} \right)0.20$ .

Step 4:

The final mixture is the sum of the first solution and second solution.

The equation for final mixture can be expressed as,

$\begin{aligned}0.375x + \left( {280 - x} \right)0.20 &= 0.30\left( {280} \right) \hfill \\0.375x + \left( {280 \times 0.20 - 0.20x} \right) &= 0.30\left( {280} \right) \hfill \\0.375x + \left( {56 - 0.20x} \right) &= 84 \hfill \\0.175x &= 28 \hfill \\\end{aligned}$

Now simplify the further solution.

$\begin{aligned}0.175x &= 28 \\x &= \frac{{28}}{{0.175}} \\x &= 160 \\\end{aligned}$

Therefore, the volume of the second solution is $160{\text{ quartz}}$ .

The volume of the first solution can be calculated as,

$280 - 160 = 120{\text{ quartz}}$

Therefore, the volume of the first solution is $120{\text{ quartz}}$ .

Learn more:

Learn more about the distance between the points link Learn more about the equivalent fractionhttps://link Learn more about midpoint of the segment link

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

Answer from: Quest

step-by-step explanation:

Answer from: Quest

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