Example Question - ratio calculation
Here are examples of questions we've helped users solve.
Ratio Calculation for Road Division
Đề bài đang hỏi về việc chia tỷ lệ cho công việc, cụ thể là phân chia một đoạn đường công mặt đất để hai phần chỉ chiếm tỷ lệ là 3/7. Để giải quyết vấn đề này, ta sẽ sử dụng một phép tính đơn giản: lấy số tỷ lệ 3 chia cho tổng số phần tỷ lệ là 7. \[ z = \frac{3}{7} \] \[ z \approx 0,4285714286 \] Kết quả này gần nhất với lựa chọn: \[ z = 0,43 \] Tuy nhiên, qua hình ảnh đề xuất, không có lựa chọn nào trùng khớp chính xác với kết quả tính toán. Lựa chọn gần nhất là z = 0,48 theo các lựa chọn được đưa ra trong hình. Có thể có một sự nhầm lẫn hoặc lỗi trong đề bài hoặc các lựa chọn đáp án nếu không có sự làm tròn nào được chỉ ra. Vậy đáp án theo tính toán chính xác nhất là z = 0,43, nhưng đáp án có thể được chấp nhận trong trường hợp này (nếu được làm tròn) là: \[ z = 0,48 \]
Calculating Ratio of Large Envelopes to Total
To find the ratio of large envelopes to the total number of envelopes, first determine the total number of envelopes by adding the number of large envelopes to the number of small envelopes. Large envelopes: 6 Small envelopes: 11 Total number of envelopes: 6 + 11 = 17 Now find the ratio of large envelopes to the total number of envelopes, which is 6 to 17. The ratio is written as: 6:17 So the correct answer is C: 6:17.
Project Time Allocation Calculation
The question states that the time spent on a project is split between planning, implementation, and quality control in the ratio 2:5:1. It is also given that 30 hours were spent on planning. Let's denote the amount of time spent on planning, implementation, and quality control as P, I, and Q, respectively. Then we have P : I : Q = 2 : 5 : 1. Since we know that 30 hours were spent on planning, P = 30. Now let's find out the total value of the parts according to the given ratio. The parts in the ratio 2:5:1 sum up to 2 + 5 + 1 = 8 parts. We know that the time spent on planning (2 parts of the ratio) corresponds to 30 hours. To find out how many hours 1 part of the ratio represents, we can divide 30 hours by the 2 parts allocated for planning: 1 part = 30 hours / 2 = 15 hours Now we can find the total time by calculating the sum of all parts of the ratio: Total time = 8 parts × 1 part's value Total time = 8 parts × 15 hours/part Total time = 120 hours Therefore, the total time the project will take to complete is 120 hours.
Finding Ratio of Triangle Areas
The given problem is to find the ratio of areas of two triangles: △AFB and △BDE. Let’s analyze the information given in the problem: - △ABE is a right-angled triangle with ∠ACB = 90°. - D and E are points on line segments BC and AC, respectively. - BD : DC = 2 : 1, meaning BD is twice as long as DC. - DC = EC = AD (since it's given that DC = EC and also DC = AD). - BE and AD intersect at F. From the given information, since BD : DC = 2 : 1, we can represent BD as 2x and DC as x for some value of x. This means BC = BD + DC = 2x + x = 3x. Given that DC = EC = AD, we can also represent each of these segments as x. Now let's find the ratio of areas of △AFB and △BDE. Note that these triangles share the same height if we consider the height to be extending from B perpendicular to AE. Therefore, the ratio of their areas will be proportional to the ratio of their bases AE and DE. Since △AFB's base AE includes AD + DE and AD = x, we have base AE = x + DE. We now need to find the length of DE. Since E is a point on AC and EC = x, AE (which is the sum of AD and DE, and we already know that AD = x) must be 2x in length since AC is the entire hypotenuse which would be twice the smaller segment EC given △ACE is a 45-45-90 right triangle due to the equality EC = AD and those are the adjacent sides of the right angle. Now we know that AE = 2x and DE is the remaining portion of AE which would equal x (since AE is 2x and AD is x, DE must be x to satisfy AE = AD + DE). Therefore, the ratio of the areas of △AFB to △BDE is proportional to their bases, which is AF to FB or AE to DE. Since AE = 2x and DE = x, the ratio of the areas is: Area(△AFB) : Area(△BDE) = AE : DE Area(△AFB) : Area(△BDE) = 2x : x Area(△AFB) : Area(△BDE) = 2 : 1 Thus, the ratio of △AFB to △BDE is 2:1.
Solving Water to Cordial Ratio with Step-by-Step Guide
Let's solve this step by step: 1. The initial ratio of water to cordial is 3:1, which means that for every 4 parts of the mixture, 3 parts are water and 1 part is cordial. 2. The initial amount of water in the concentrated cordial is given as 360 ml. 3. To find the amount of cordial, we divide the water by 3 (since the ratio of water to cordial is 3:1): cordial = 360 ml / 3 = 120 ml 4. So initially, we have 360 ml of water and 120 ml of cordial in the mixture. 5. We want to get a new water to cordial ratio of 7:1, which means for every 8 parts of the new mixture, 7 parts should be water. 6. Since the amount of cordial is not changing (remaining at 120 ml), we need to find how much water will give us the 7:1 ratio: cordial = 120 ml = 1 part (from the new ratio 7:1) We can say that 1 part (the cordial) corresponds to 120 ml, so 7 parts (water) would correspond to: water_new = 7 * 120 ml = 840 ml 7. The amount of water that needs to be added to achieve this new ratio is the difference between the new amount of water needed (840 ml) and the initial amount of water (360 ml): water_needed = 840 ml - 360 ml = 480 ml To the nearest milliliter, 480 ml of water needs to be added to the mixture to have a non-concentrated cordial with a water-to-cordial ratio of 7:1.
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