Direct AND Inverse Variation Word Problems

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other. It can be expressed as y = kx, where k is a non-zero constant.

Front

What is inverse variation?

Back

Inverse variation is a relationship between two variables where the product of the two variables is a constant. It can be expressed as y = k/x, where k is a non-zero constant.

Front

If y varies directly with x and y = 12 when x = 15, what is the constant of variation (k)?

Back

k = y/x = 12/15 = 0.8.

Front

If y = kx and k = 2, what is y when x = 10?

Back

y = 2 * 10 = 20.

Front

If 12 workers can complete a job in 5 days, how many days will it take 6 workers to complete the same job?

Back

It will take 10 days for 6 workers to complete the job.

Front

If 8 oranges cost $10.40, what is the cost of 1 orange?

Back

The cost of 1 orange is $10.40 / 8 = $1.30.

Front

If a person earns $70 for 5 hours of work, how much do they earn per hour?

Back

They earn $70 / 5 = $14 per hour.

Front

If y varies directly with x and y = 16 when x = 20, what is y when x = 10?

Back

y = (16/20) * 10 = 8.

Front

If the number of workers is doubled, how does that affect the time taken to complete a job?

Back

If the number of workers is doubled, the time taken to complete the job is halved, assuming all workers work at the same rate.

Front

If a car travels 60 miles in 1 hour, how far will it travel in 3 hours?

Back

The car will travel 60 miles/hour * 3 hours = 180 miles.