Solving Word Problems with Systems of Equations

In this video, host Brian Heisler explains how to solve systems of equations presented as word problems. He covers two examples: one involving Mark and Stacy's mileage and another about the Ford and Carter family's activity costs. The video demonstrates using substitution and elimination methods to solve these problems, emphasizing the importance of identifying key information in word problems.

What is the first step in solving a word problem involving systems of equations?

• Writing random equations

• Identifying the important information

• Guessing the answer

• Ignoring the numbers

If Mark and Stacy ran a total of 70 miles, and Stacy ran 20 miles more than Mark, what is the equation representing their total distance?

• M + S = 100

• M + S = 70

• M + S = 90

• M + S = 50

In the equation S = M + 20, what does 'S' represent?

• The difference in their distances

• Stacy's total distance

• Mark's total distance

• The total distance run by both

After substituting S = M + 20 into M + S = 70, what is the simplified equation?

• 2M + 20 = 70

• M + 20 = 70

• M + 2S = 70

• 2M + 40 = 70

What is Mark's running distance after solving the equation 2M + 20 = 70?

• 15 miles

• 20 miles

• 30 miles

• 25 miles

How many miles did Stacy run if Mark ran 25 miles?

• 45 miles

• 35 miles

• 30 miles

• 40 miles

What is the total cost for the Ford family for two adults and three children?

• $150

• $122

• $86

• $100

What method is used to solve the second example involving the Ford and Carter families?

• Elimination

• Trial and Error

• Graphing

• Substitution

What is the cost per child if the total cost for three adults and four children is $122?

• $16

• $10

• $12

• $14

What is the final cost per adult in the second example?

• $22

• $20

• $26

• $24