Test your knowledge with 9 questions about rule of three simple. Be sure to check the step-by-step resolution after the feedback to answer your questions.
question 1
To help a family on vacation in Paris, a hotel receptionist gave a map of the city and explained that the distance of 4 cm on the map represented 600 m in the real landscape.
To take a walk that corresponds to a path of 12 cm on the map, how many meters would the family travel in the city?
a) 1200 m
b) 2400 m
c) 1800 m
d) 3600 m
Correct alternative: c) 1800 m.
Note that in the statement of the question we were given three values, which we will use to calculate the unknown value represented with the unknown x.
| Distance on map | real distance |
| 4 cm | 600 m |
| 12 cm | x |
Note that these quantities are directly proportional, because if we increase the distance on the map, consequently, the space covered in the city will be greater.
Thus, the distance covered in the city will be 1800 meters, which corresponds to 12 cm on the map.
question 2
Márcia decided to offer a snack to homeless people in her city. For this, she decided to make sandwiches and went to the bakery near her house, where a kilogram of French bread costs R$12.00.
Knowing that Márcia had R$ 42.00 to buy bread, how many kilos did she manage to buy?
a) 4.5 kg
b) 3.5 kg
c) 4 kg
d) 3 kg
Correct alternative: b) 3.5 kg.
According to the statement, as a kilo of bread costs R$ 12.00, so the more money Márcia uses, the more bread she will be able to buy. Therefore, we have a question with magnitudes directly proportional and we will call the amount purchased by Marcia x.
| kg of bread | Price |
| 1 | BRL 12.00 |
| x | BRL 42.00 |
Therefore, with R$ 42.00 Márcia managed to buy 3.5 kg of French bread.
question 3
Bruno would like to buy a video game, which the view had a 30% discount and, therefore, reduced R$ 60.00 from the purchase price. The other form of payment offered by the store was to buy on the card in a single installment with a 12% discount.
If Bruno chose to pay for the video game with the card, what is the value in reais of the discount granted?
a) BRL 24.00
b) BRL 18.00
c) BRL 22.00
d) BRL 14.00
Correct alternative: a) R$ 24.00.
Note that the lower the discount percentage, the smaller the amount subtracted from the video game price. Therefore, this problem involves magnitudes directly proportional.
| Percentage | discount amount |
| 30% | BRL 60.00 |
| 12% | x |
Therefore, when choosing card as a payment method, Bruno will have a 12% discount which in reais corresponds to R$ 24.00.
question 4
Antônio has a hamburger shop with 5 delivery guys. With the coronavirus pandemic in 2020 and the containment measures in his city increased the number of orders for home delivery, so he hired 8 more couriers.
Knowing that, on average, 5 couriers during the period of operation of the establishment delivered 45 snacks, how many orders can the new team meet at the same time?
a) 170
b) 219
c) 120
d) 117
Correct alternative: d) 117.
Please note that the more couriers on the team, the more snacks can be delivered. Therefore, we have a problem involving quantities directly proportional.
The new team will have the 5 deliverymen who are already part of the establishment and 8 more hired, in other words, a total of 13.
| Deliverymen | Number of snacks |
| 5 | 45 |
| 13 | x |
Therefore, with the hiring of 8 more delivery people, it will be possible to deliver 117 snacks during the period when the burger shop is open.
question 5
Julia is a seamstress and to make 8 skirts of the same size she uses 16 meters of fabric. If she received an order for 22 skirts for a store, how many yards of fabric does she need to buy?
a) 52
b) 44
c) 36
d) 54
Correct alternative: b) 44.
The greater the number of skirts to sew, the more fabric will be needed and, therefore, the magnitudes of the situation presented are directly proportional.
| Fabric (m) | skirts |
| 16 | 8 |
| x | 22 |
Therefore, Julia will need 44 meters of fabric to make the pieces ordered.
question 6
The increase in the demand for hospital supplies made more truck drivers hired by a distributor to reduce the number of trips of the 2 trucks used until then.
If with 4 trucks of the same size, 8 trips were needed, how many trips were the company's 2 trucks doing to deliver the same number of goods?
a) 12
b) 14
c) 16
d) 18
Correct alternative: c) 16.
If the quantity of goods was the same, then with fewer trucks it was necessary to make more trips with the material, that is, we have quantities inversely proportional.
| number of trucks | Number of trips |
| 4 | 8 |
| 2 | x |
Therefore, with 2 trucks, 16 trips were made to distribute the material.
question 7
Carla has 3 cats and uses a feed pack to feed them for 30 days. Upon returning home, she found two cats on the street and decided to adopt them. Now, with 5 cats, how many days will a pack of kibble be enough to feed them?
a) 13
b) 16
c) 15
d) 18
Correct alternative: d) 18.
Note that the more Carla cats you have, the less time a pack of food will last, as there will be more animals to feed. Therefore, the quantities presented in the problem are inversely proportional.
| Cats | Days |
| 3 | 30 |
| 5 | x |
Therefore, for 5 cats a pack of kibble will be needed to feed them for 18 days.
question 8
Community health agents are professionals who, among their functions, are committed to combating one of the most frequent diseases in Brazil: dengue. To do this, the agents go from house to house to identify outbreaks of mosquito development Aedes aegypti and guide the residents.
Knowing that 12 professionals need 28 days to visit all houses in 3 neighborhoods of a city, how long does it take for a quarter of the team to visit the same houses?
a) 90
b) 98
c) 120
d) 112
Correct alternative: d) 112.
First, we must calculate how many professionals represent a quarter of the team. For this, we will multiply the fraction ¼ by the total number of health agents.
Now that we know how many professionals there are, we can set up the table and analyze the magnitudes involved in the problem.
| health agents | Days |
| 12 | 28 |
| 3 | x |
Note that the fewer people working, the more days it will take to be able to visit all the houses in the 3 neighborhoods, so the magnitudes are inversely proportional.
Therefore, a quarter of the team will be able to visit every house in the 3 districts of the city in 112 days.
question 9
Paul was taking his son to take the Enem test. For the chosen route, if the vehicle had a speed of 70 km/h, it would take about 1h30 to reach the place where the test was to take place.
If the speedometer of the car Paulo was driving marked a speed of 85 km/h, how much time, approximately, in minutes, did Paulo save by going faster?
a) 12
b) 16
c) 14
d) 10
Correct alternative: b) 16.
Note that the greater the speed of the car, the less time it takes to make the journey. Thus, the problem involves magnitudes inversely proportional.
As an hour has sixty minutes, an hour and thirty minutes corresponds to an hour and a half, which can be written 1.5 hours.
| Speed | Time |
| 70 km/h | 1.5 h |
| 85 km/h | x |
To find out how much time Paul saved, we must subtract the value of x found from normal time.
1.5 h - 1.23 h = 0.27 h
Now we perform a simple rule of three to convert hours to minutes.
| hours | minutes |
| 1h | 60 min |
| 0.27h | y |
Therefore, Paulo saved approximately 16 minutes by increasing the speed.
Get more knowledge with the contents:
- Simple and compound rule of three
- rule of three compound
- Exercises on rule of three
- Rule of Three Compound Exercises
- Exercises on reason and proportion