Julia and Luis decided to save money for the summer and have different plans to save. Julia saves R$ 10 per week, while Luis saves R$ 2 per week and an additional R$ 3 per week. After a few weeks, they both saved the same amount of money. a) Write a system of equations involving the number of weeks and the amount saved by Julia and Luis. b) Solve the system of equations to determine the number of weeks in which they would both save the same amount. c) Use the Cartesian plane to represent Julia and Luis' savings and indicate the point of intersection.

Maria and João are friends and together they have a total of R$ 28.00 to spend at a snack bar. Knowing that Maria has R$ 6.00 less than João, can you create a system of first-degree equations with two unknowns to represent this situation? What is the amount of money each one has?

The ages of Felipe and Márcia 8 years ago were in the ratio of 3 to 7. Today, they are in the ratio of 5 to 9. The sum of Felipe and Márcia's current ages is:

To solve this question, follow the steps below: 1. Let F be Felipe's current age and M be Márcia's current age. 2. First, analyze the information about the ratio of ages 8 years ago. This data can be expressed by the equation: (F-8) / (M-8) = 3/7 3. Now, analyze the information about the ratio of current ages. This data can be expressed by the equation: F / M = 5/9 4. From equation (2), we can isolate one of the variables, for example, F: F = (5/9)M 5. Substitute equation (4) into equation (1): ((5/9)M - 8) / (M - 8) = 3/7 6. To solve the equation, multiply both sides by 63 (least common multiple of 9 and 7) to eliminate the fractions: 63 * ((5/9)M - 8) = 63 * (3/7)(M - 8) 7. Simplifying the terms: 35M - 504 = 27M - 216 8. Now, solve the linear equation: 35M - 27M = 216 - 504 8M = -288 M = -288 / 8 M = 36 9. Substitute the value of M into equation (4) to find the value of F: F = (5/9)(36) F = 20 10. Finally, the sum of Felipe and Márcia's current ages is: F + M = 20 + 36 = 56 years Therefore, the correct answer is "56 years".

The figure represents the floor of a living room that is in the shape of a square. This floor is made up of rectangular wooden tiles, all congruent to each other. The area of the room is 36 square meters. The perimeter, in meters, of each tile is equal to

The area of the room is 36 square meters and, as the room is square, each side measures the square root of 36, which is 6 meters. Since the floor is made up of rectangular and congruent wooden tiles, each tile is 1 meter in length (6 tiles fill one side of the room). The perimeter of each tile is calculated by adding all sides (1m + 1m + 1m + 1m), resulting in 4 meters. However, as the tile is rectangular, one of the sides is smaller. If we divide the perimeter by 4, we get 1 meter for each longer side and, for the sum to still be 4, each shorter side must measure 0.5 meters. Therefore, the perimeter of each tile is 3 meters.

João and Maria are saving money to buy a gift for their mother. They decide to save part of their weekly allowances to reach the necessary amount. João saves R$ x per week and Maria saves R$ y per week. At the end of three weeks, João saved R$ 60 and Maria saved R$ 45 after two weeks. Set up the system of equations that represents this situation and find the values of x and y.

Question bank: System of Equations

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