João is saving his allowance to buy a toy that costs R$ 50.00. He has already saved R$ 10.00. If he saves the same amount of money every month, how many months does he need to save money to be able to buy the toy?

João and Maria decided to have a bike race. João covered a distance of 15 km in 30 minutes, while Maria covered a distance of 20 km in the same time. Based on this data, who had the fastest bike? Justify your answer using the concept of ratios and proportions.

João and Maria are playing with toy cars. João's car travels 2 meters in 4 seconds, while Maria's car travels 5 meters in 10 seconds. Considering the distance traveled and the time for each car, identify who has the faster car and explain why, using the concept of ratio.

A father decided to divide an inheritance of R$ 60,000.00 among Ana, 7 years old, Paula, 3 years old, and Carlos, 2 years old. This division would be in parts directly proportional to their ages. The amount that Ana should receive in reais is

To solve this question, we should follow these steps: 1. Identify the ages of each one: Ana = 7 years, Paula = 3 years, and Carlos = 2 years. 2. Calculate the sum of the ages: 7 + 3 + 2 = 12. 3. Identify the total inheritance: R$ 60,000.00. 4. Calculate the ratio of the parts directly proportional to each one's age. The ratio is the age of each one divided by the sum of the ages: - Ana's Ratio: 7/12 - Paula's Ratio: 3/12 - Carlos's Ratio: 2/12 5. Now, we must calculate the amount that each one will receive by multiplying each one's ratio by the total inheritance: - Ana's Amount: (7/12) * 60,000 = R$ 35,000.00 - Paula's Amount: (3/12) * 60,000 = R$ 15,000.00 - Carlos's Amount: (2/12) * 60,000 = R$ 10,000.00 6. Check if the sum of the amounts each one will receive is equal to the total inheritance: 35,000 + 15,000 + 10,000 = R$ 60,000.00. 7. The amount that Ana should receive, according to the solution found in step 5, is R$ 35,000.00. Therefore, the correct answer is "35,000".

A pool can hold 36000 liters of water when fully filled. Due to an unidentified leak, 900 liters of water are added every three days to maintain the level. The fraction of water that represents the daily leak and the water replenishment, in liters, done in 9 days are, respectively,

Let's solve the question step by step:

1. Notice that every 3 days 900 liters of water are added to the pool. Therefore, to find the amount of water replenished in 9 days, simply multiply 900 liters by 3 (since 9 days are three times 3 days). So, we have:

900 liters * 3 = 2700 liters

Thus, the water replenishment done in 9 days is 2700 liters.

2. Now, let's calculate the fraction of water that represents the daily leak. We know that every 3 days 900 liters of water are added to the pool, so the daily leak is:

Daily leak = (900 liters / 3 days) = 300 liters/day

3. To find the fraction of water that represents the daily leak, simply divide the daily leak (300 liters) by the total capacity of the pool (36000 liters):

Fraction of the daily leak = (300 liters) / (36000 liters) = 1/120

Therefore, the fraction of water that represents the daily leak is 1/120 and the water replenishment done in 9 days is 2700 liters.

Question bank: Reasons and Proportions

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