Basic Algebra and Word Problems

Using the quadratic formula, x = (-b ± √(b² - 4ac)) / 2a, where a = 1, b = -5, and c = 6, we get x = (5 ± √(25 - 24)) / 2 = (5 ± 1) / 2. Therefore, x = 2 or x = 3.

The first train travels for 1 hour before the second train leaves. In that time, it travels 70 mph * 1 hour = 70 miles. Therefore, the distance between the two trains at 11:00 AM is 900 miles - 70 miles = 830 miles. The two trains are traveling towards each other at a combined speed of 70 mph + 80 mph = 150 mph. Therefore, they will meet in 830 miles / 150 mph = 5.53 hours after 11:00 AM, which is 2:00 PM.

There are 60 women and 40 men in the company. 20% of the women are promoted, which is 0.2 * 60 = 12 women. 30% of the men are promoted, which is 0.3 * 40 = 12 men. Therefore, the total number of employees promoted is 12 + 12 = 24.

The area of a rectangle is length * width. Therefore, (x + 2)(x - 3) = 24. Expanding the brackets, we get x^2 - x - 6 = 24. Rearranging, we get x^2 - x - 30 = 0. Factoring, we get (x - 6)(x + 5) = 0. Therefore, x = 6 or x = -5. Since the length of the garden cannot be negative, x = 6.

The discount is 20% of $20, which is 0.2 * $20 = $4. Therefore, the sale price of the shirt is $20 - $4 = $16.

Let the distance between City A and City B be x miles. The time taken for the journey from City A to City B is x / 60 hours, and the time taken for the journey from City B to City A is x / 75 hours. The total time taken for the round trip is the sum of these two times, which is (x / 60) + (x / 75) = 5 hours. Solving for x, we get x = 200 miles.

There are 60 women and 40 men in the company. 20% of the women are promoted, which is 0.2 * 60 = 12 women. 30% of the men are promoted, which is 0.3 * 40 = 12 men. Therefore, the total number of men promoted is 12.

The area of a rectangle is length * width. Therefore, the area of the room is 12 feet * 8 feet = 96 square feet.

The first train travels for 1 hour before the second train leaves. In that time, it travels 70 mph * 1 hour = 70 miles. Therefore, the distance between the two trains at 11:00 AM is 900 miles - 70 miles = 830 miles. The two trains are traveling towards each other at a combined speed of 70 mph + 80 mph = 150 mph. Therefore, they will meet in 830 miles / 150 mph = 5.53 hours after 11:00 AM, which is 2:00 PM.

There are 60 women and 40 men in the company. 20% of the women are promoted, which is 0.2 * 60 = 12 women. 30% of the men are promoted, which is 0.3 * 40 = 12 men. Therefore, the total number of employees promoted is 12 + 12 = 24.

The area of a rectangle is length * width. Therefore, (x + 2)(x - 3) = 24. Expanding the brackets, we get x^2 - x - 6 = 24. Rearranging, we get x^2 - x - 30 = 0. Factoring, we get (x - 6)(x + 5) = 0. Therefore, x = 6 or x = -5. Since the length of the garden cannot be negative, x = 6.

The discount is 20% of $20, which is 0.2 * $20 = $4. Therefore, the sale price of the shirt is $20 - $4 = $16.

Let the distance between City A and City B be x miles. The time taken for the journey from City A to City B is x / 60 hours, and the time taken for the journey from City B to City A is x / 75 hours. The total time taken for the round trip is the sum of these two times, which is (x / 60) + (x / 75) = 5 hours. Solving for x, we get x = 200 miles.