Question

Антон, Боря и Варя бросали баскетбольный мяч в корзину. Каждый сделал 5 бросков. Все попали мячом в корзину разное число раз, а всего оказалось 10 попаданий. Боря попал мячом в корзину больше всех. 1) Сколько раз попал мячом в корзину Боря? 2) Известно , что Варя попала мячом в корзину на один раз больше , чем Антон. Сколько раз попал мячом в корзину Антон?

Answer 1

Тут может быть несколько вариантов например Антон - 2 , Варя-3,Боря-5
Антон -1,Варя-2,Боря -7
Антон-0,Варя-1,Боря-9

Answer 2

Боря - 5 раз
Варя - 3 раза
Антон - 2 раза

Answer 3

Problem Analysis

We are given that Anton, Borya, and Varya made 5 basketball shots each into the basket. They each made a different number of shots, but the total number of shots made was 10. We need to determine how many shots Borya made and how many shots Anton made.

Solution

Let's assume that Anton made x shots, Borya made y shots, and Varya made z shots. We know that x + y + z = 10 because the total number of shots made was 10.

We are also given that Borya made more shots than anyone else. Therefore, y > x and y > z.

We are also given that Varya made one more shot than Anton. Therefore, z = x + 1.

Using these equations, we can solve for the values of x, y, and z.

Solution Steps

1. Start with the equation x + y + z = 10. 2. Substitute z = x + 1 into the equation to get x + y + (x + 1) = 10. 3. Simplify the equation to get 2x + y + 1 = 10. 4. Rearrange the equation to get y = 10 - 2x - 1. 5. Simplify the equation to get y = 9 - 2x. 6. Since y > x, we can conclude that y must be greater than or equal to 6 (because if y = 5, then x would be negative, which is not possible). 7. We also know that y + x + 1 = 10 (from the equation x + y + z = 10 and z = x + 1). 8. Substitute y = 9 - 2x into the equation to get 9 - 2x + x + 1 = 10. 9. Simplify the equation to get 10 - x = 10. 10. Solve for x to get x = 0. 11. Substitute x = 0 into the equation y = 9 - 2x to get y = 9 - 2(0) = 9. 12. Substitute x = 0 into the equation z = x + 1 to get z = 0 + 1 = 1.

Solution

Based on the above calculations, we can conclude that: 1. Borya made 9 shots. 2. Anton made 0 shots.

Therefore, Borya made the most shots, and Anton did not make any shots.

Answer

1. Borya made the basketball into the basket 9 times. 2. Anton made the basketball into the basket 0 times.

Note: The above solution is based on the given information and the assumption that each person made a different number of shots.