Direct and Inverse Word Problems

Front

What does it mean for a quantity to be directly proportional to another quantity?

Back

A quantity is directly proportional to another if an increase in one quantity results in a proportional increase in the other. This relationship can be expressed as y = kx, where k is a constant.

Front

What is the formula to calculate the total earnings based on hours worked when earnings are directly proportional to hours?

Back

Total earnings can be calculated using the formula: Total Earnings = (Earnings per hour) x (Number of hours worked).

Front

How do you determine the number of workers needed to complete a job in a shorter time frame when the work is directly proportional to the number of workers?

Back

To find the number of workers needed, use the formula: Workers needed = (Original workers x Original time) / New time.

Front

What is the relationship between the number of workers and the time taken to complete a job?

Back

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

Front

How do you calculate the number of days taken for a different number of workers to complete the same job?

Back

Use the formula: Days taken = (Original days x Original workers) / New workers.

Front

What does it mean for a quantity to vary inversely with another quantity?

Back

A quantity varies inversely with another if an increase in one quantity results in a proportional decrease in the other. This relationship can be expressed as y = k/x, where k is a constant.

Front

How do you find the width of a rectangle when its width varies inversely with its length?

Back

Use the formula: Width = k/Length, where k is a constant determined by the initial width and length.

Front

What is the relationship between a person's mass and the amount of water in their body?

Back

The amount of water in a person's body varies directly with their mass, meaning as mass increases, the amount of water also increases.

Front

How do you calculate the amount of water in a person based on their mass?

Back

Use the formula: Water content = (Water per kg) x (Mass), where Water per kg is determined from initial data.

Front

What is the significance of constants in direct and inverse proportionality?

Back

Constants (k) in direct and inverse proportionality represent the fixed ratio between the quantities involved.