Age Relationships and Equations

The video tutorial explains how to solve a classic age word problem involving two people, William and Ben. It starts by defining variables to represent their ages and sets up equations based on given conditions. The tutorial walks through the algebraic steps to solve for Ben's current age and verifies the solution by checking the conditions. The problem-solving process is structured and encourages viewers to attempt solving it independently before following along.

What is the relationship between William's and Ben's ages as stated in the problem?

• William is twice as old as Ben.

• William is three times as old as Ben.

• William is four times as old as Ben.

• William is five times as old as Ben.

Which variable is used to represent Ben's current age?

• x

• y

• w

• b

How is Ben's age 12 years ago expressed in terms of the variable b?

• b + 12

• b - 12

• 12b

• b/12

What equation represents the relationship between William's and Ben's ages 12 years ago?

• 7(b - 12) = 4b + 12

• 4(b - 12) = 7b - 12

• 7(b - 12) = 4b - 12

• 4(b - 12) = 7b + 12

What is the first step in solving the equation 7(b - 12) = 4b - 12?

• Add 12 to both sides

• Subtract 4b from both sides

• Distribute the 7

• Divide both sides by 7

After distributing the 7 in the equation, what is the next step?

• Divide both sides by 7

• Multiply both sides by 3

• Subtract 4b from both sides

• Add 84 to both sides

What is the value of b after solving the equation?

• 24

• 36

• 12

• 48

What is William's age now if Ben is 24 years old?

• 72

• 96

• 84

• 108

How old was William 12 years ago?

• 96

• 108

• 84

• 72

What is the significance of verifying the solution in this problem?

• To verify the arithmetic operations

• To confirm the ages match the given conditions

• To ensure the equation is set up correctly

• To check if the variables are defined properly