SOLVING DIRECT AND INVERSE PROPORTION WORD PROBLEMS

Problem 1 :

Karen earns $28.50 for working 6 hours. If the amount m she earns varies with h the number of hours she works, how much she earns for working 10 hours?

Solution:

It comes under direct proportion.

28.50 ⋅ 10 = x ⋅ 6

x = (28.50 ⋅10) / 6

x = 285/6

x = $47.5

She is earning $47.5 for 10 hours.

Problem 2 :

A bottle of 150 vitamins costs $5.25. If the cost varies directly with the number of vitamins in the bottle, what should a bottle of 250 vitamins cost?

Solution:

Let x be the cost of 250 vitamins bottle.

It comes under direct proportion.

5.25 ⋅ 250 = x ⋅ 150

x = (5.25 ⋅ 250) / 150

x = 1312.5/150

x = 8.75

So, cost of 250 vitamins bottle is $8.75.

Problem 3 :

For a fixed number of miles, the gas mileage of a car (miles/gallon) varies inversely with the number of gallons. Stephen's truck averaged 24 miles per gallon and used 750 gallons of gas in one year. If the next year, to rive the same number of miles, Stephen drove a compact car averaging 39 miles per gallon, how many gallons of gas would he use?

Solution:

It comes under inverse proportion.

24 ⋅ 750 = 39 ⋅ x

x = (24 ⋅ 750)/39

x = 461.5 gallons

So, he is using 461.5 gallons of gas.

Problem 4 :

Wei received $55.35 in interest on a $1230 in her bank account. If the interest varies directly with the amount deposited, how much would Wei receive for the same amount of time if she had $2000 in her account?

Solution:

It comes under direct proportion.

1230 ⋅ x = 2000 ⋅ 55.35

x = (2000 ⋅ 55.35)/1230

x = 90

So, he will earn the interest of $90.

Problem 5 :

The number of gallons g of fuel used on a trip varies directly with the number of miles m traveled. If a trip of 270 miles required 12 gallons of fuel, how many gallons are required for a trip of 400 miles?

Solution:

It comes under direct proportion.

12 ⋅ 400 = x ⋅ 270

x = (12 ⋅ 400) / 270

x = 17.7 gallons

So, 17.7 gallons is required for a trip of 400 miles.

Problem 6 :

The time it takes to travel a fixed distance varies inversely with the speed traveled. If it takes Pam 40 minutes to bike to her fishing spot at 9 miles per hour, how long will it take her if she rides at 12 miles per hour?

Solution:

It comes under inverse proportion.

Here the distance to be covered in both cases is the same.

9 ⋅ 40 = 12 ⋅ x

x = (9 ⋅ 40) / 12

x = 360/12

x = 30 minutes

So, he can cover the same distance in 30 minutes.

Problem 7 :

The time needed to paint a fence varies directly with the length of the fence. If it takes 5 hours to paint 200 feet of fence, how long will it take to paint 500 feet of fence?

Solution:

It comes under direct proportion.

200 ⋅ x = 500 ⋅ 5

x = (500 ⋅ 5)/200

x = 2500/200

x = 12.5 hrs

So, it will take 12.5 hours.

Problem 8 :

The number of bricks laid varies directly with the amount of time spent. If 45 bricks are laid in 65 minutes, how much time would it take to lay 500 bricks?

Solution:

1 bricks are laid = 65/45 = 13/9 min

Then 500 bricks are laid = (13/9 × 500) min

= 6500/9

= (6500/9) × 60 min

= 12 hr 3 min

So, it will take 12 hr 3 min to lay 500 bricks.