Word problems and solution

Solving mixture problems generally involves solving systems of equations. Mixture problems are ones in which two different solutions are mixed together, resulting in a new, final solution. Using a table will help to set up and solve these problems. The basic structure of this table is shown below:

The first column in the table (Name) is used to identify the fluids or objects being mixed in the problem. The second column (Amount) identifies the amounts of each of the fluids or objects. The third column (Value) is used for the value of each object or the percentage of concentration of each fluid. The last column (Equation) contains the product of the Amount times the Value or Concentration.

With mixture problems, there is often mixing with a pure solution or using water, which contains none of the chemical of interest. For pure solutions, the concentration is 100%. For water, the concentration is 0%. This is shown in the following example.

Questions

For questions 1 to 9, write the equations that define the relationship.

1. A tank contains 8000 litres of a solution that is 40% acid. How much water should be added to make a solution that is 30% acid?
2. How much pure antifreeze should be added to 5 litres of a 30% mixture of antifreeze to make a solution that is 50% antifreeze?
3. You have 12 kilograms of 10% saline solution and another solution of 3% strength. How many kilograms of the second should be added to the first in order to get a 5% solution?
4. How much pure alcohol must be added to 24 litres of a 14% solution of alcohol in order to produce a 20% solution?
5. How many litres of a blue dye that costs [latex]$1.60[/latex] per litre must be mixed with 18 litres of magenta dye that costs [latex]$2.50[/latex] per litre to make a mixture that costs [latex]$1.90[/latex] per litre?
6. How many grams of pure acid must be added to 40 grams of a 20% acid solution to make a solution which is 36% acid?
7. A 100-kg bag of animal feed is 40% oats. How many kilograms of pure oats must be added to this feed to produce a blend of 50% oats?
8. A 20-gram alloy of platinum that costs [latex]$220[/latex] per gram is mixed with an alloy that costs [latex]$400[/latex] per gram. How many grams of the [latex]$400[/latex] alloy should be used to make an alloy that costs [latex]$300[/latex] per gram?
9. How many kilograms of tea that cost [latex]$4.20[/latex] per kilogram must be mixed with 12 kilograms of tea that cost [latex]$2.25[/latex] per kilogram to make a mixture that costs [latex]$3.40[/latex] per kilogram?

Solve questions 10 to 21.

1. How many litres of a solvent that costs [latex]$80[/latex] per litre must be mixed with 6 litres of a solvent that costs [latex]$25[/latex] per litre to make a solvent that costs [latex]$36[/latex] per litre?
2. How many kilograms of hard candy that cost [latex]$7.50[/latex] per kg must be mixed with 24 kg of jelly beans that cost [latex]$3.25[/latex] per kg to make a mixture that sells for [latex]$4.50[/latex] per kg?
3. How many kilograms of soil supplement that costs [latex]$7.00[/latex] per kg must be mixed with 20 kg of aluminum nitrate that costs [latex]$3.50[/latex] per kg to make a fertilizer that costs [latex]$4.50[/latex] per kg?
4. A candy mix sells for [latex]$2.20[/latex] per kg. It contains chocolates worth [latex]$1.80[/latex] per kg and other candy worth [latex]$3.00[/latex] per kg. How much of each are in 15 kg of the mixture?
5. A certain grade of milk contains 10% butterfat and a certain grade of cream 60% butterfat. How many litres of each must be taken so as to obtain a mixture of 100 litres that will be 45% butterfat?
6. Solution A is 50% acid and solution B is 80% acid. How much of each should be used to make 100 cc of a solution that is 68% acid?
7. A paint that contains 21% green dye is mixed with a paint that contains 15% green dye. How many litres of each must be used to make 600 litres of paint that is 19% green dye?
8. How many kilograms of coffee that is 40% java beans must be mixed with coffee that is 30% java beans to make an 80-kg coffee blend that is 32% java beans?
9. A caterer needs to make a slightly alcoholic fruit punch that has a strength of 6% alcohol. How many litres of fruit juice must be added to 3.75 litres of 40% alcohol?
10. A mechanic needs to dilute a 70% antifreeze solution to make 20 litres of 18% strength. How many litres of water must be added?
11. How many millilitres of water must be added to 50 millilitres of 100% acid to make a 40% solution?
12. How many litres of water need to be evaporated from 50 litres of a 12% salt solution to produce a 15% salt solution?

Answer Key 6.8

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Frequently Asked Questions (FAQ)

• How do you solve word problems?

• To solve word problems start by reading the problem carefully and understanding what it’s asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.

• How do you identify word problems in math?

• Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.

• Is there a calculator that can solve word problems?

• Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.

• What is an age problem?

• An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as «x years ago,» «in y years,» or «y years later,» which indicate that the problem is related to time and age.

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