Exploring Proportions and Cross Multiplying

The video tutorial explains how to solve a word problem using proportions. It involves calculating the number of gallons of gas needed for a 525-mile trip, given that 21 gallons are used for 150 miles. The instructor demonstrates setting up a proportion, using cross multiplication, and solving the resulting algebraic equation to find the unknown value. The solution reveals that 73.5 gallons are needed for the trip.

What is the first step in solving the word problem mentioned?

• Identify the unknown value.

• Perform cross-multiplication.

• Set up a proportion.

• Divide both sides of the equation.

What does the numerator in the proportion represent?

• The number of gallons used.

• The price of gas per gallon.

• The unknown value.

• The distance traveled in miles.

What mathematical concept is primarily used to solve the word problem?

• Multiplication

• Addition

• Subtraction

• Proportion

What is the purpose of setting up a proportion in this problem?

• To determine the duration of the trip.

• To calculate the speed of the trip.

• To find the relationship between miles and gallons.

• To compare prices of gas.

Why is cross-multiplication used in solving the proportion?

• To simplify the equation.

• To add complexity to the problem.

• To isolate the variable.

• To eliminate the denominator.

What is the result of cross-multiplying the given proportion?

• 21x = 150 * 525

• 150x = 525 / 21

• 150x = 21 * 525

• 525x = 150 * 21

How is the variable 'x' isolated in the equation?

• By dividing both sides by 150.

• By multiplying both sides by 525.

• By subtracting 21 from both sides.

• By adding 150 to both sides.

What does 'x' represent in the context of the problem?

• The cost of gas per gallon.

• The number of gallons needed.

• The distance traveled in miles.

• The total cost of the trip.

How many gallons of gas would Paul use for a 525-mile trip?

• 525 gallons

• 150 gallons

• 73.5 gallons

• 21 gallons

What does the final answer, 73.5 gallons, indicate?

• The cost of the gas used.

• The distance traveled per gallon.

• The number of stops needed for gas.

• The total amount of gas needed for the trip.