Algebraic word problems are mathematical problems that require the use of algebraic equations to solve real-world situations presented in written or verbal form.
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Algebraic word problems are a type of mathematical problem that require the use of algebraic equations to solve real-world situations. They can be presented in written or verbal form, and can cover a wide range of topics, including finance, physics, biology, and more.
As renowned mathematician and philosopher René Descartes once said, “Geometry is the foundation of all sciences.” Algebra, which is the study of mathematical symbols and the rules for manipulating these symbols, is a fundamental building block of geometry and other mathematical fields. Algebraic word problems allow individuals to use algebra to solve real-world problems, making it a pivotal tool in many industries.
Some interesting facts about algebraic word problems:
- Algebra was first developed by Arabian mathematicians in the early Middle Ages.
- The word “algebra” comes from the Arabic word “al-jabr,” which means “the reunion of broken parts.”
- Algebraic equations use letters (known as variables) to represent unknown values, allowing individuals to solve for these values using mathematical operations.
- Word problems are often used in educational settings to help students apply mathematical concepts to real-world scenarios.
- Algebraic word problems can be found in a wide variety of industries and professions, from finance and engineering, to computer science and physics.
To better understand algebraic word problems, it can be helpful to see an example. Here is a sample problem along with the steps needed to solve it:
Problem: A train is traveling north at 60 miles per hour. At the same time, another train is traveling west at 45 miles per hour. If the two trains are 100 miles apart to start, how far apart will they be after 2 hours?
Step 1: Define the variables. Let x represent the distance traveled by the northbound train, and y represent the distance traveled by the westbound train.
Step 2: Write equations based on the information given. We can use the formula Distance = Rate x Time to create two equations: x = 60t (northbound train) and y = 45t (westbound train), where t is the number of hours since the start.
Step 3: Solve for the variables. We know that the two trains start 100 miles apart, which means that x² + y² = 100². We can substitute the equations above to get (60t)² + (45t)² = 100², which simplifies to 5t² = 400. Solving for t, we get t = 4.
Step 4: Calculate the final answer. Now that we know t, we can substitute back into the equations for x and y to get x = 240 and y = 180. Using the distance formula again, we get √((240-0)² + (180-0)²) ≈ 300 miles. Therefore, the two trains will be approximately 300 miles apart after 2 hours.
Algebraic word problems can be challenging, but with practice and patience, anyone can learn to solve them and apply their math skills to the real world.
See a related video
In the “Algebraic Word Problems” video, Professor Dave illustrates how algebraic equations can be used to solve word problems. He presents real-life scenarios and demonstrates how to assign variables and construct equations based on the given information. He then shows how to solve the equations by algebraic manipulation to obtain the answers to the problems.
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Algebraic word problems are questions that require translating sentences to equations, then solving those equations. The equations we need to write will only involve. basic arithmetic operations. and a single variable. Usually, the variable represents an unknown quantity in a real-life scenario.
Algebraic word problems are questions that require translating sentences to equations, then solving those equations. The equations we need to write will only involve basic arithmetic operations and a single variable. Usually, the variable represents an unknown quantity in a real-life scenario.
Algebra Word Problems
- Unit Rate Problem: Problem: You buy 5 pounds of apples for $3.75. What is the unit rate of a pound of apples?
- “Find the Numbers” Word Problems: Problem: The sum of two numbers is 18.
Furthermore, people ask
Similarly, What are some examples of algebra problems?
For example.
| 1. | -5y+3=2(4y+12) |
|---|---|
| 4. | |x-a|= a2-x2 |
| 5. | 4 x 2 + 1 − 2 x 2 + 2 = 8 |
| 6. | log2(2x-1)+x=log4(144) |
| 7. | { x 2 + y 2 = 17 + 2 x ( x − 1 ) 2 + ( y − 8 ) 2 = 34 |
Besides, What are the different types of word problems in algebra? Answer to this: Students often complain that word problems are the most difficult part of algebra. But there are ways to make them easier to figure out. I see them as four main groups with some overlap: Translations, Structures, Assumed Knowledge, and Formulas. Within each are several types.
Consequently, What is an example of an algebraic expression word? For example, the phrase "the sum of three times a number and five" translates to "3x + 5," while the phrase "three times the sum of a number and five" translates to "3(x + 5)."
Also, How do you write an algebraic equation for a word problem?
In reply to that: The price of a visit to the dentist is fifty. Dollars if the dentist fills any cavities an additional charge of one hundred dollars per cavity gets added to the bill. If the dentist finds n cavities.
In this regard, What are algebra word problems worksheets?
In algebra word problems worksheets, we will talk about algebra, which is a branch of mathematics dealing with symbols and the rules for manipulating these symbols. They represent quantities without fixed values, known as variables. Solving algebraic word problems requires us to combine our ability to create and solve equations.
Also asked, What is a word problem in math?
The reply will be: A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you’ve ever taken a math class, you’ve probably solved a word problem. For instance, does this sound familiar? Johnny has 12 apples.
Moreover, What is the answer to an algebraic sentence?
Answer will be: Looks like everything checks out, so the answer to our algebraic sentence is the number 1. Example 5: Two-thirds of the sum of three times a number and six is ten. What is the number? This problem involves a fraction and an algebraic expression as you can tell.
In this manner, How do you solve word problems?
The reply will be: 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.
Additionally, What are algebra word problems worksheets? Response to this: In algebra word problems worksheets, we will talk about algebra, which is a branch of mathematics dealing with symbols and the rules for manipulating these symbols. They represent quantities without fixed values, known as variables. Solving algebraic word problems requires us to combine our ability to create and solve equations.
What is a word problem in math?
As a response to this: A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you’ve ever taken a math class, you’ve probably solved a word problem. For instance, does this sound familiar? Johnny has 12 apples.
Beside this, What is the answer to an algebraic sentence? Looks like everything checks out, so the answer to our algebraic sentence is the number 1. Example 5: Two-thirds of the sum of three times a number and six is ten. What is the number? This problem involves a fraction and an algebraic expression as you can tell.
Consequently, How do you solve word problems? Answer: 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.