In this section, we will explore various solved problems related to proportionality. These problems are designed to illustrate how to identify and apply proportional relationships in different contexts. Through practical examples and detailed explanations, we will address how to solve proportionality problems using effective methods and techniques.

1

Calculate the unknown term in the following proportion

 

Solution

In a proportion, the product of the means equals the product of the extremes.

 

 

2

Calculate the unknown term in the following proportion

 

Solution

In a proportion, the product of the means equals the product of the extremes.

 

 

3

Calculate the unknown term in the following proportion

 

Solution

In a proportion, the product of the means equals the product of the extremes.

 

 

4

Calculate the unknown term in the following proportion

 

Solution

In a proportion, the product of the means equals the product of the extremes.

 

 

5

Calculate the unknown term in the following proportion

 

Solution

In a proportion, the product of the means equals the product of the extremes.

 

 

6

Two wheels are connected by a transmission belt. The first has a radius of 9.8 inches and the second of 29.5 inches. When the first has made 300 turns, how many turns will the second have made?

Solution

These are inversely proportional quantities, since a larger radius will make fewer turns

 

Then we have the following inverse proportion rule

7

Two gears are synchronized with each other. The first has 25 teeth and the second 10. When the second gear has made 50 turns, how many turns will the first have made?

Solution

These are inversely proportional quantities, since fewer teeth will make more turns

 

 

Then we have the following inverse proportion rule

 

8

Four people cook 50 dishes in 3 hours. If one of the people gets sick, how long will it take the three people to prepare the 50 dishes?

Solution

Fewer people means more time, so this is an indirect proportion

 

 

Then we have the following indirect proportion rule

 

9

Six people can stay in a hotel for 12 days for $950. How much will the hotel cost for 15 people for eight days?

Solution

More people and more days means more money, so this is a direct proportion



 

Then we have the following direct proportion rule

10

If with 12 cans of of paint each, 295 feet of fence 31.5 inches high have been painted. Calculate how many cans of of paint will be needed to paint a similar fence high and long.

Solution

More quarts of paint means fewer cans, so this is an inverse proportion

More means more cans, so this is a direct proportion


Then we have the following proportion rule

11

workers plow a rectangular field long and wide in days. How many workers will be needed to plow another similar field long by wide in five days?

Solution

More surface area means more workers, so this is a direct proportion

More days means fewer workers, so this is an inverse proportion.


Then we have the following proportion rule

12

Six faucets take hours to fill a tank with capacity. How many hours will four faucets take to fill tanks of each?

Solution

More faucets means fewer hours, so this is an inverse proportion.

More tanks means more hours, so this is a direct proportion.

More means more hours, so this is a direct proportion.

Then we have the following proportion rule

13

Of the students in a school, have gone on a trip. What percentage of students have gone on a trip?

Solution

We will apply direct proportion


Then we have the following proportion rule

14

When purchasing a vehicle whose price is , we get a discount of %. How much do we have to pay for the vehicle?

Solution

We start by doing the following proportion operation

Then we have the following proportion rule

-

It can also be calculated directly as follows:

There is a discount of %, that is, for every we pay less, therefore instead of the we pay .


Then we have the following proportion rule

15

The price of a computer is without tax. How much do we have to pay for it if the tax is %?

Solution

Due to tax there is a surcharge of %, that is, for every we pay more, therefore instead of the we pay


Then we have the following proportion rule

16

When buying a monitor that costs we get a discount of . How much do we have to pay?

Solution

There is a discount of %, that is, for every we pay less, therefore instead of the we pay .


Then we have the following proportion rule

17

An item is sold with a profit of % over the cost price. If it was purchased for , find the selling price.

Solution

Due to profit there is a surcharge of % over the cost price, that is, for every you pay more, therefore instead of the you pay


Then we have the following proportion rule

18

What price should we mark on an item whose purchase cost to gain % when selling it?

Solution

If the purchase price is and you gain %, the selling price will be .


Then we have the following proportion rule

19

What selling price should we put on an item purchased for , to lose % on the selling price?

Solution

If the selling price is and you lose %, the purchase price will be .


20

An object is sold losing % on the purchase price. Find the selling price of said item whose purchase value was .

Solution

If the purchase price is and you lose %, the selling price will be .


Then we have the following proportion rule

📌 Find the best math course on Superprof. Choose between an online math teacher or an in-person one for your classes.

Did you like this article? Rate it!

5.00 (2 Note(n))
Loading...

Agostina Babbo

Agostina Babbo is an English and Italian to Spanish translator and writer, specializing in product localization, legal content for tech, and team sports—particularly handball and e-sports. With a degree in Public Translation from the University of Buenos Aires and a Master's in Translation and New Technologies from ISTRAD/Universidad de Madrid, she brings both linguistic expertise and technical insight to her work.