Solving Systems of Equations in Real-World Scenarios

The video tutorial addresses common challenges students face with word problems, focusing on solving systems of equations involving two variables. It covers three types of problems: a distance problem with a plane and wind speed, a mixture problem with acid solutions, and a finance problem involving investments and interest rates. The instructor demonstrates how to set up and solve these problems using elimination and substitution methods, providing step-by-step guidance and encouraging practice to recognize patterns in similar problems.

What is the first step in solving a word problem involving two variables and two equations?

• Guess the answer

• Set up the equations

• Ignore the problem

• Solve the equations directly

In the plane and wind speed problem, what equation represents the plane's speed with a headwind?

• R + W = 100

• R - W = 100

• R - W = 800

• R + W = 800

How long did it take for the plane to travel back to its starting point with the wind?

• 10 hours

• 6 hours

• 4 hours

• 8 hours

What is the rate of the plane in still air?

• 150 miles per hour

• 50 miles per hour

• 200 miles per hour

• 100 miles per hour

In the acid mixture problem, what is the total volume of the final solution?

• 10 gallons

• 20 gallons

• 15 gallons

• 25 gallons

What is the percentage of acid in the final solution?

• 20%

• 30%

• 10%

• 40%

How many gallons of the 40% acid solution are needed?

• 20 gallons

• 15 gallons

• 10 gallons

• 5 gallons

What is the total amount invested in the two certificates of deposit?

• $20,000

• $5,000

• $10,000

• $15,000

What is the interest rate of the second certificate of deposit?

• 5%

• 3.5%

• 4%

• 2.5%

How much was invested in the 5% certificate of deposit?

• $2,000

• $4,000

• $6,000

• $8,000