Constant of Proportionality Word Problems

Front

What is the constant of proportionality?

Back

The constant of proportionality is the ratio between two quantities that are directly proportional to each other. It is often represented as 'k' in the equation y = kx.

Front

How do you find the constant of proportionality from a word problem?

Back

To find the constant of proportionality, identify the two quantities that are proportional, divide one quantity by the other, and express the result as a ratio.

Front

If 4 books cost $20, what is the cost of 1 book?

Back

The cost of 1 book is $5, calculated by dividing the total cost by the number of books: $20 / 4 = $5.

Front

If 5 workers can complete a project in 10 days, how many days would it take 10 workers to complete the same project?

Back

It would take 5 days for 10 workers to complete the project, as doubling the number of workers halves the time required.

Front

What is the formula to calculate the total cost based on the number of items and the cost per item?

Back

The formula is Total Cost = Number of Items × Cost per Item.

Front

In a proportional relationship, if one quantity increases, what happens to the other quantity?

Back

In a proportional relationship, if one quantity increases, the other quantity also increases, maintaining the same ratio.

Front

How can you determine how many boxes a truck can transport in a different number of trips?

Back

To determine how many boxes a truck can transport in a different number of trips, use the ratio of boxes to trips and multiply by the new number of trips.

Front

If a car travels 240 miles in 4 hours, what is its speed in miles per hour?

Back

The speed is 60 miles per hour, calculated by dividing the distance by the time: 240 miles / 4 hours = 60 mph.

Front

What is the relationship between workers and time in completing a project?

Back

The relationship is inversely proportional; as the number of workers increases, the time taken to complete the project decreases.

Front

How do you set up a proportion to solve a word problem?

Back

To set up a proportion, identify the two ratios that are equal and write them as a fraction equation, then cross-multiply to solve.