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.

Tags

CCSS.HSF-LE.A.1B

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).

Tags

CCSS.HSF-BF.A.1A

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.

Tags

CCSS.6.EE.B.7

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.

Tags

CCSS.HSF-LE.A.1B

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.

Tags

CCSS.HSF-LE.A.1B

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.

Tags

CCSS.HSF-LE.A.1B