Geometry and Algebra Word Problems

The video tutorial covers solving systems of equations through practical examples. It begins with finding two numbers based on their sum and difference using the elimination method. Next, it tackles a rectangle perimeter problem, using substitution to find the length and width. Finally, it compares rental costs of two vehicles to determine the mileage at which costs are equal, again using substitution. The tutorial emphasizes different methods for solving systems of equations, including elimination and substitution, and demonstrates their application in real-world scenarios.

What is the elimination method primarily used for in solving systems of equations?

• To find the sum of two numbers

• To eliminate one variable by adding or subtracting equations

• To substitute one equation into another

• To graph the equations

If the sum of two numbers is 93 and their difference is 9, what are the numbers?

• 45 and 48

• 50 and 43

• 51 and 42

• 52 and 41

What is the formula for the perimeter of a rectangle?

• 2 * Length + Width

• Length * Width

• 2 * (Length + Width)

• Length + Width

If the width of a rectangle is 4 more than half its length, which equation represents this relationship?

• Width = Length + 4

• Width = 1/2 * Length + 4

• Width = 2 * Length + 4

• Width = Length - 4

What is the length of the rectangle if its perimeter is 160 yards and the width is 4 more than half the length?

• 70 yards

• 60 yards

• 50 yards

• 80 yards

How do you express 75 cents in dollars?

• $0.75

• $0.075

• $7.50

• $75.00

What is the fixed cost for renting the 18-foot truck from Sunset?

• $0.75 per mile

• $0.50 per mile

• $59.95

• $49.95

At what mileage will the cost of renting from Sunset and Cactus be the same?

• 50 miles

• 60 miles

• 40 miles

• 30 miles

Which method is highlighted for solving the cost comparison problem?

• Trial and Error

• Substitution

• Elimination

• Graphing

What is the variable cost per mile for the Cactus van?

• $0.50

• $0.25

• $1.00

• $0.75