Question

Экзамен по математике содержал три задачи: по алгебре, по геометрии и по тригонометрии. Из 800 абитуриентов задачу по алгебре решили 250 человек, по алгебре или геометрии - 660 человек; по две задачи решили 400 человек, из них две задачи по алгебре и геометрии решили только 150 человек, по алгебре и тригонометрии 50 человек. Только по тригонометрии задачи решили 120 человек. Ни один абитуриент не решил все задачи; 20 абитуриентов не решили ни одной задачи. Сколько абитуриентов решили задачи по геометрии? Сколько абитуриентов решили только одну задачу?

Answer 1

По геометрии решили задачи 660-250=410, 800-20-400=380-решили только 1 задачу.

Answer 2

X0+Xа+Xг+Хт+Хаг+Хат+Хгт+Хагт=800 Xа+Хаг+Хат+Хагт=250 Xа+Xг+Хаг+Хат+Хгт+Хагт=660 Хаг+Хат+Хгт=400 Хаг=150 Хат=50 Хагт=0 X0=20 Хт=120 Xа+Xг+Хт=? Xг=? после подстановки Хаг=150,Хат=50,Хагт=0,X0=20,Хт=120 20+Xа+Xг+120+150+50+Хгт+Хагт=800 (1) Xа+150+50+0=250 (2) Xа+Xг+150+50+Хгт+0=660 (3) 150+50+Хгт=400 (4) Ха=50 (из 2) Хгт=200 (из 4) 50+Xг+150+50+200+0=660 (3) Хг=210 Xа+Xг+Хт=50+210+120=380

Answer 3

Problem Analysis

To solve this problem, we need to determine the number of students who solved the geometry problem and the number of students who solved exactly one problem. We are given the following information:

- Total number of students: 800 - Number of students who solved the algebra problem: 250 - Number of students who solved either algebra or geometry: 660 - Number of students who solved two problems: 400 - Number of students who solved both algebra and geometry: 150 - Number of students who solved both algebra and trigonometry: 50 - Number of students who solved only the trigonometry problem: 120 - No student solved all three problems - 20 students did not solve any problem

Solution

Let's break down the problem step by step to find the number of students who solved the geometry problem and the number of students who solved exactly one problem.

Step 1: Find the number of students who solved both algebra and geometry. - We are given that 150 students solved both algebra and geometry.

Step 2: Find the number of students who solved both algebra and trigonometry. - We are given that 50 students solved both algebra and trigonometry.

Step 3: Find the number of students who solved only the trigonometry problem. - We are given that 120 students solved only the trigonometry problem.

Step 4: Find the number of students who solved only the geometry problem. - To find this, we need to subtract the number of students who solved both algebra and geometry (150) and the number of students who solved both algebra and trigonometry (50) from the total number of students who solved either algebra or geometry (660). - Number of students who solved only the geometry problem = Total number of students who solved either algebra or geometry - Number of students who solved both algebra and geometry - Number of students who solved both algebra and trigonometry = 660 - 150 - 50 = 460

Step 5: Find the number of students who solved exactly one problem. - To find this, we need to subtract the number of students who solved two problems (400) from the total number of students (800). - Number of students who solved exactly one problem = Total number of students - Number of students who solved two problems = 800 - 400 = 400

Answer

Based on the given information, we can conclude that: - The number of students who solved the geometry problem is 460. - The number of students who solved exactly one problem is 400.

Please let me know if you need any further clarification or assistance!