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Solving 7th grade math problems on page 58 of Wings of Kite with step-by-step solutions for exercises 1, 2, 3... from the lesson 'Equal Ratio Sequences'. This is a helpful resource to ensure correct problem-solving, grasp concepts securely, and reinforce lesson knowledge.
Explore various study materials for mastering Grade 7 Mathematics:
- Access the complete set of Solving 7th Grade Math problems with Wings of Kite
- Solving 7th Grade Math problems on page 28 of Knowledge Connect Textbook - Exercise 5: Getting acquainted with infinite recurring decimals
- Solving 7th Grade Math problems on pages 33, 34 of Creative Horizon Textbook - Exercise 1: Irrational Numbers. Square root of a numerical value
Solving 7th grade math problems on page 58 of Wings of Kite
Exercise 6. Equal Ratio Sequences
1. Solve Exercise 1 Page 58 Math Textbook Grade 7
2. Solve Exercise 2 Page 58 Math Textbook Grade 7
Answer Key:
3. Solve Exercise 3 Page 58 Math Textbook Grade 7
Step-by-step solution:
Answer Key:
4. Solve Exercise 4 Page 58 Math Textbook Grade 7
Problem Statement: The amount of carbon dioxide absorbed and the amount of oxygen released into the environment by 1 square meter of plant leaves during photosynthesis for 11 hours in direct sunlight are in the ratio of 11 to 8. Calculate the amount of carbon dioxide and oxygen absorbed and released by 1 square meter of plant leaves during photosynthesis for 11 hours in direct sunlight, knowing that the amount of carbon dioxide absorbed by the leaves is 8 grams more than the amount of oxygen released into the environment.
Solution Guide:
Let the amount of carbon dioxide absorbed and the amount of oxygen released into the environment by 1 square meter of plant leaves during photosynthesis for 11 hours in direct sunlight be x and y respectively.
Represent the given conditions of the problem in formulaic form.
Apply the properties of equal ratio sequences to find x, y.
Answer:
Let the amount of carbon dioxide absorbed and the amount of oxygen released into the environment by 1 square meter of plant leaves during photosynthesis for 11 hours in direct sunlight be x, y (g) (x, y > 0).
Since the amount of carbon dioxide absorbed and the amount of oxygen released into the environment by 1 square meter of plant leaves during photosynthesis for 11 hours in direct sunlight are in the ratio of 11 to 8,
As the amount of carbon dioxide absorbed by the leaves exceeds the amount of oxygen released into the environment by 8 grams in 11 hours, we have x - y = 8.
Applying the properties of equal ratio sequences, we have:
5. Solve Exercise 5 Page 58 Math Textbook Grade 7
Solution Guide:
+ Let the lengths of the two sides of the rectangle be x and y (x, y > 0).
+ Represent the given conditions of the problem in terms of x, y.
+ Apply the properties of equal ratio sequences to find x, y.
+ Calculate the area of the rectangle.
Answer:
Let the lengths of the two sides of the rectangle be x and y (m) (x, y > 0).
Since the perimeter of the plot of land is 48 m, then 2.(x + y) = 48. Thus, x + y = 48 : 2 = 24.
Applying the properties of equal ratio sequences, we have:
Therefore,
So, the area of the rectangle is: S = 9.15 = 135 (m2)
6. Solve Exercise 6 Page 58 Math Textbook Grade 7
Problem Statement: During the charity campaign to support flood victims, the number of books donated by three classes 7A, 7B, 7C is in the ratio of 5:6:8. Calculate the total number of books donated by all three classes, knowing that the number of books donated by class 7C exceeds the number of books donated by class 7A by 24 books.
Solution Guide:
+ Let the number of books donated by classes 7A, 7B, 7C be x, y, z respectively (books)
+ Represent the given conditions of the problem in terms of x, y, z.
+ Apply the properties of equal ratio sequences to find x, y, z.
Answer:
Let the number of books donated by classes 7A, 7B, 7C be x, y, z respectively (books)
Since the number of books donated by classes 7A, 7B, 7C is in the ratio of 5:6:8,
As the number of books donated by class 7C exceeds the number of books donated by class 7A by 24 books, then z - x = 24.
Applying the properties of equal ratio sequences, we have:
Therefore,
So, the number of books donated by classes 7A, 7B, 7C are respectively 40 books, 48 books, and 64 books.
7. Solve Exercise 7 Page 58 Math Textbook Grade 7
Problem Statement: On the Truong Sa archipelago of Vietnam, the phoenix tree, square banyan tree, and ironwood tree are resilient species, able to withstand the destruction of nature, saltwater, and have long growth periods. On the occasion of Tet, the soldiers planted a total of 192 phoenix trees, square banyan trees, and ironwood trees on the islands. The number of phoenix trees, square banyan trees, and ironwood trees planted is in the ratio of 5:4:3. Calculate the number of each type of tree planted by the soldiers.
Solution Guide:
+ Let the number of phoenix trees, square banyan trees, and ironwood trees planted be x, y, z respectively (trees)
+ Represent the given conditions of the problem in terms of x, y, z.
+ Applying the properties of equal ratio sequences, find x, y, z.
Answer:
Let the number of phoenix trees, square banyan trees, and ironwood trees planted be x, y, z respectively (trees)
Since the total number of trees planted is 192 trees, then x + y + z = 192.
Since the number of phoenix trees, square banyan trees, and ironwood trees planted is in the ratio of 5:4:3, we have:
So, the number of phoenix trees, square banyan trees, and ironwood trees planted are: 80 trees, 64 trees, and 48 trees respectively.
With the math resource 'Solving 7th Grade Math Problems Page 58 Volume 1 Cánh Diều Book', students can effectively solve problems involving Equal Ratio Sequences as well as solidify their understanding of the lesson.
Reference Exercises:
- Solve Math 7 Page 62, 63 Volume 1 Cánh Diều Book - Exercise 7. Direct Proportion Quantity
- Solve Math 7 Page 68 Volume 1 Cánh Diều Book - Exercise 8. Indirect Proportion Quantity
