Question

Готовились к олимпиаде по математике Максим в субботу и воскресенье решил задачи.В субботу он решил 7/18 всех задач,а в воскресенье 2/9 всех задач и остальные 14 задач.Сколько всего задач решил Максим за два дня.

Answer 1

36

14 / ( 1 - 2/9 ) = 18 - осталось после субботы

18 / (1 - 7/18) = 36 -решил максим

Answer 2

Answer in detail. Maxim prepared for the math olympiad on Saturday and Sunday and solved problems. On Saturday he solved 7/18 of all the problems, and on Sunday 2/9 of all the problems and the remaining 14 problems. How many problems did Maxim solve in two days?

To answer this question, we need to find the total number of problems that Maxim had to solve. Let us denote this number by x. Then we can write the following equation:

$$\frac{7}{18}x + \frac{2}{9}x + 14 = x$$

This equation can be simplified by multiplying both sides by 18:

$$7x + 4x + 252 = 18x$$

Then we can subtract 11x from both sides and get:

$$252 = 7x$$

Finally, we can divide both sides by 7 and obtain:

$$x = 36$$

Therefore, the total number of problems that Maxim had to solve was 36. Since he solved 7/18 of them on Saturday and 2/9 of them on Sunday, we can calculate how many problems he solved each day:

$$\frac{7}{18} \times 36 = 14$$ $$\frac{2}{9} \times 36 = 8$$

Hence, Maxim solved 14 problems on Saturday and 8 problems on Sunday. The sum of these numbers is the answer to the question:

$$14 + 8 = 22$$

So, Maxim solved 22 problems in two days.