Word problems involving linear equations in one variable.
•Number problems
•Age problems
•Rate problems
•Mixture problems
i need examples of this
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Word problems involving linear equations in one variable.
•Number problems
•Age problems
•Rate problems
•Mixture problems
i need examples of this
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Answer:
Number problems:
Example: The sum of two numbers is 15. If one of the numbers is 6 more than the other, what are the two numbers?
Let x be the smaller number, then the larger number is x + 6.
The sum of the two numbers is 15, so we can write an equation: x + (x + 6) = 15
Simplifying the equation, we get: 2x + 6 = 15
Subtracting 6 from both sides, we get: 2x = 9
Dividing both sides by 2, we get: x = 4.5
Therefore, the two numbers are 4.5 and 10.5.
Age problems:
Example: The sum of the ages of a father and his son is 50. If the father is 3 times as old as his son, how old is each?
Let x be the age of the son, then the age of the father is 3x.
The sum of their ages is 50, so we can write an equation: x + 3x = 50
Simplifying the equation, we get: 4x = 50
Dividing both sides by 4, we get: x = 12.5
Therefore, the son is 12.5 years old and the father is 3 times as old, or 37.5 years old.
Rate problems:
Example: A car travels 300 miles in 5 hours. What is the average speed of the car in miles per hour?
Let x be the average speed of the car in miles per hour.
We know that distance = rate x time, so we can write an equation: 300 = x * 5
Simplifying the equation, we get: x = 60
Therefore, the average speed of the car is 60 miles per hour.
Mixture problems:
Example: A chemist has a solution that is 20% acid. How many liters of pure acid must be added to 5 liters of the solution to obtain a solution that is 40% acid?
Let x be the number of liters of pure acid to be added.
The amount of acid in the original 5 liters of solution is 0.2 * 5 = 1 liter.
After adding x liters of pure acid, the total amount of solution will be 5 + x liters.
The amount of acid in the final solution is (1 + x) liters.
The concentration of acid in the final solution is 40%, so we can write an equation: (1 + x)/(5 + x) = 0.4
Multiplying both sides by (5 + x), we get: 1 + x = 2 + 0.4x
Simplifying the equation, we get: 0.6x = 1
Dividing both sides by 0.6, we get: x = 1.67
Therefore, 1.67 liters of pure acid must be added to 5 liters of the solution to obtain a solution that is 40% acid.