How To Set Up Proportion Word Problems

Proportion word problems

There are lots of situations that tin can create proportion word problems. We will illustrate these situations with some examples.

Trouble # 1

Mix 3 liters of water with 4 lemons to brand lemonade. How many liters of h2o are mixed with 8 lemons.

Set up the ratios, only make sure that the two ratios are written in the aforementioned order.

For example, all the followings can be used to solve this problem:

Let x be number of liters of water.

three / 4

x / 8

4 / 3

8 / x

3 / x

four / 8

x / 3

8 / 4

iii / 4

x / 8

4 / 3

viii / 10

three / ten

iv / 8

ten / 3

8 / 4

It is very important to discover that if the ratio on the left is a ratio of number of liters of water to number of lemons, you lot have to practice the same ratio on the right before you set up them equal.

Look carefully and you will see that this is what the kickoff proportion does.

However, the 2d proportion focuses on a ratio of number of lemons to number of liter of water.

Number of lemons / Number of liters of water

Number of lemons / Number of liters of h2o

When solving proportion give-and-take problems, brand certain it is gear up correctly. One time you gear up your proportion correctly, all you lot take to do if to supplant values that you lot know and use an x or any other variable for the value yous don't know.

Let us solve the second proportion. I already showed you how to solve a proportion. If you lot do non remember, get to solving proportions.

Let fifty exist the number of lemons and allow due west be the number of liters of water.

When solving proportion word problems, make sure it is ready correctly. In one case you lot ready your proportion correctly, all you accept to do if to supercede values that y'all know and apply an x or any other variable for the value you don't know.

Let usa solve the second proportion. I already showed you how to solve a proportion. If you practise non retrieve, become to solving proportions.

Cross production is usually used to solve proportion word bug. If y'all do a cross product, you will become:

iv × x = 3 × viii

4 × x = 24. Since four × half-dozen = 24, x = half dozen

6 liters should be mixed with eight lemons.

More interesting proportion word problems

Problem # two

A male child who is iii feet tall can cast a shadow on the basis that is 7 feet long. How alpine is a human who tin cast a shadow that is 14 anxiety long?

Ready the proportion by doing ratios of peak to length of shadow.

Proportion word problem

Meridian of boy / Length of shadow

Height of man / Length of shadow

Replace the known values and use H for the unknown height of the human being

Cross multiply

3 × 14 = seven × H

42 = vii × H

Since 7 × 6 = 42, H = 6

The man is 6 feet alpine

Problem # three

3 gallons of paint cover 900 square feet. How many gallons will embrace 300 square anxiety?

iii / 900

x / 300

900 / 3

300 / x

3 / ten

900 / 300

x / 3

300 / 900

Nosotros volition solve the showtime one:

Doing cantankerous product, will give you 3 × 300 = x × 900

900 = x × 900. Thus x = i because 1 × 900 = 900.

Problem # 4: Firewoman math and proportion

A fire-eater truck tin can concur 3000 gallons of h2o. A fire-eater can deliver 160 gallons of water every ii minutes.

1. How much water volition be delivered in 10 minutes?

2. How long will it take for the fire-eater to empty the tank?

ane. Set up a proportion by doing ratios of number of gallons to time it takes

Number of gallons / Time it takes

Replace the known values and use G to represent the numbers of gallons in ten minutes

Cross multiply

160 × 10 = 2 × G

1600 = 2 × G

Since 2 × 800 = 1600, Chiliad = 800

800 gallons of water volition be delivered in x minutes

ii. Set up a proportion by doing ratios of number of gallons to time it takes

Number of gallons / Time it takes

Supersede the known values and utilize T to represent the fourth dimension it takes to deliver 3000 gallons.

Cross multiply

160 × T = ii × 3000

160 × T = 6000

Separate 6000 past 160 to become T. 6000 divided past 160 = 37.v

T = 37.5 or 37 minutes and 30 seconds.

I welcome whatsoever questions about these proportion word problems if you have any.

Superlative of boy / Length of shadow

Peak of human / Length of shadow

Replace the known values and use H for the unknown height of the man.

Cross multiply

3 × 14 = 7 × H

42 = 7 × H

Since seven × six = 42, H = 6

The man is 6 feet alpine

Problem # iii

3 gallons of paint cover 900 foursquare feet. How many gallons will cover 300 foursquare feet?

3 / 900

x / 300

900 / three

300 / x

3 / 10

900 / 300

We will solve the starting time one:

Doing cross product, volition give you iii × 300 = x × 900

900 = 10 × 900. Thus x = i because 1 × 900 = 900.

Problem # 4: Fireman math and proportion

A firefighter truck can hold 3000 gallons of water. A firefighter can deliver 160 gallons of water every 2 minutes.

one. How much water volition exist delivered in 10 minutes?

2. How long will information technology take for the firewoman to empty the tank?

1. Set upwardly a proportion past doing ratios of number of gallons to time it takes

# of gallons / Fourth dimension information technology takes

# of gallons / Time it takes

Supercede the known values and apply Grand to represent the numbers of gallons in 10 minutes.

Cross multiply

160 × ten = 2 × Grand

1600 = 2 × Thousand

Since ii × 800 = 1600, 1000 = 800

800 gallons of water will be delivered in 10 minutes.

2. Prepare a proportion by doing ratios of number of gallons to time it takes.

# of gallons / Fourth dimension it takes

# of gallons / Time it takes

Replace the known values and use T to represent the fourth dimension it takes to deliver 3000 gallons.

Cantankerous multiply

160 × T = 2 × 3000

160 × T = 6000

Separate 6000 by 160 to get T. 6000 divided past 160 = 37.5

T = 37.5 or 37 minutes and 30 seconds

I welcome any questions about these proportion word problems if y'all have any.

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