Solve mixture problems with proportions quick check connections academy

Answer 1

Sure! Mixture problems typically involve finding the concentration or amount of substances in a mixture based on given proportions. Here’s a general approach to solving these types of problems, along with a quick example to illustrate.

Steps to Solve Mixture Problems:

1. Identify the substances involved: Determine what is being mixed and their respective amounts/concentrations.

2. Set up a proportion or equation: Use the concept of ratios and proportions to set up an equation based on the information given.

3. Solve for the unknown: Isolate the variable you need to find and solve the equation.

4. Check your answer: Ensure that the solution fits into the context of the problem and makes sense logically.

Example Problem:

Problem: You have a 10% salt solution and a 30% salt solution. If you mix 4 liters of the 10% solution with $x$ liters of the 30% solution, how much of the 30% solution do you need to make a 20% salt solution?

Solution Steps:

1. Identify the components:

   • Amount of 10% solution = 4 liters.
   • Concentration of 10% solution = 0.10.
   • Amount of 30% solution = $x$ liters.
   • Concentration of 30% solution = 0.30.
   • Desired concentration after mixing = 20%.

2. Set up the equation: The total amount of salt in the mix equals the total concentration of the salt in the resulting mixture.

   $$\text{Salt from 10\% solution}+\text{Salt from 30\% solution}=\text{Salt in resulting solution}$$

   This can be expressed as:

   $$(0.10)(4)+(0.30)(x)=(0.20)(4+x)$$

3. Simplify and solve for $x$:

   $$0.4+0.30x=0.8+0.20x$$

   Rearranging gives:

   $$0.30x-0.20x=0.8-0.4$$

   $$0.10x=0.4$$

   Solving for $x$:

   $$x=\frac{0.4}{0.10}=4$$

4. Conclusion: You need to mix 4 liters of the 30% solution with the 4 liters of the 10% solution to achieve a 20% salt solution.

General Tips:

• Always double-check your calculations.
• Ensure the units are consistent.
• Pay attention to the final concentration, as it must fit logically within the context of the problem.

If you have a specific mixture problem you'd like help with, feel free to share!