Question

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?

Answer 1

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 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,

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

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,

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

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,

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

Consider $x$ 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 can be written as 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 evaluated as,

$280 - 160 = 120{\text{ quartz}}$  

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

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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

Answer 2

Answer:

120 and 160

Step-by-step explanation: