Algebra Word Problems Worksheet with Solutions

Algebra is a subject that often poses challenges for students, especially when it comes to word problems. If you are a student or parent seeking a reliable resource to practice and improve algebraic problem-solving skills, consider utilizing algebra word problems worksheet with solutions. These worksheets can provide valuable practice exercises and step-by-step solutions to help you grasp difficult concepts and enhance your understanding of algebraic equations and problem-solving techniques.

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A boat travels upstream at a speed of 8 km/h and downstream at a speed of 12 km/h. Calculate the speed of the current.

To calculate the speed of the current, we use the formula where speed of the boat in still water is the average of its upstream and downstream speeds. Therefore, the speed of the current is half of the difference between the downstream and upstream speeds, which is (12 km/h - 8 km/h) / 2 = 2 km/h. Hence, the speed of the current is 2 km/h.

The sum of two numbers is 24, and their difference is 8. Find the numbers.

Let x and y be the two numbers. Given that the sum of the numbers is 24, we have the equation x + y = 24. Also, the difference between the numbers is 8, so we have the equation x - y = 8. Solving these two equations simultaneously, we get x = 16 and y = 8. Therefore, the two numbers are 16 and 8.

The perimeter of a rectangle is 36 cm. If its length is 2 cm longer than its width, find the dimensions of the rectangle.

Let x be the width of the rectangle. Since the length is 2 cm longer than the width, the length would be x + 2. The perimeter of a rectangle is calculated by the formula P = 2*(length + width), which in this case is 36 cm. Substituting the values and simplifying, we get 36 = 2*((x + 2) + x). This simplifies to 36 = 2*(2x + 2), which further simplifies to 36 = 4x + 4. Solving for x, we get x = 8. Therefore, the width of the rectangle is 8 cm and the length is 10 cm.

A salesperson earns a commission of 5% on each sale. If they earned $500 in commission, what was the total value of their sales?

The total value of the sales made by the salesperson would be $10,000 ($500 / 0.05). This means that if the salesperson earned $500 in commission at a rate of 5% for each sale, the total value of their sales was $10,000.

The sum of three consecutive odd integers is 165. Determine the integers.

Let the three consecutive odd integers be represented by x, x+2, and x+4. Adding them together, x + (x+2) + (x+4) = 165. Simplifying this equation leads to 3x + 6 = 165. Solving for x gives x = 53. Therefore, the three integers are 53, 55, and 57.

A car travels a distance of 480 km in 6 hours. What is its average speed?

The average speed of the car is 480 km divided by 6 hours, which equals 80 km per hour.

An investment grows at an annual interest rate of 4%. If the initial investment was $2000, what will be the value after 5 years?

After 5 years, the investment will have grown to $2433.72.

It takes 32 workers 8 days to complete a project. How many days would it take for 48 workers to complete the same project?

If 32 workers complete a project in 8 days, then it means that the total work required for the project is 32 workers x 8 days = 256 worker-days. To determine how long 48 workers would take to complete the same project, we can use the concept of worker-days. With 48 workers, it would take 256 worker-days / 48 workers = 5.33 days for 48 workers to complete the project. However, since they cannot complete a fraction of a day, it would take 6 days for 48 workers to complete the project.

A rectangle's length is triple its width. If the area of the rectangle is 54 cm², find its dimensions.

Let's denote the width of the rectangle as x cm. Since the length is triple the width, the length would be 3x cm. The area of a rectangle is given by length multiplied by width, which in this case is (3x)(x) = 54 cm². By solving the equation 3x² = 54, we find x = ?18 cm ? 4.24 cm. Therefore, the dimensions of the rectangle are width = 4.24 cm and length = 3(4.24) = 12.72 cm.

A company's revenue is $10,000 and its expenses are $8,500. Determine the company's profit.

The company's profit can be calculated by subtracting expenses from revenue. So, by subtracting $8,500 (expenses) from $10,000 (revenue), the company's profit would be $1,500.