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. Сколько раз попал мячом в корзину Боря? Известно, что Варя попала мячом в корзину на один раз больше, чем Антон. Сколько раз попал мячом в корзину Антон?

Answer 1

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

Answer 2

Problem Analysis

We are given that Anton, Borya, and Varya made 5 basketball shots each. They all made a different number of shots, but the total number of shots made was 10. Borya made the most shots, and Varya made one more shot than Anton. We need to determine how many shots Borya made and how many shots Anton made.

Solution

Let's assume that Anton made x shots. Since Varya made one more shot than Anton, Varya made x + 1 shots. The total number of shots made by Anton, Borya, and Varya is 10, so we can write the equation:

x + (x + 1) + Borya = 10

We also know that Borya made the most shots, so we can assume that Borya made y shots, where y > x + 1.

Now we can solve the equation to find the values of x and y.

Solving the Equation

Let's substitute the value of Borya's shots (y) into the equation:

x + (x + 1) + y = 10

Simplifying the equation:

2x + y + 1 = 10

Rearranging the equation:

2x + y = 9 ---(Equation 1)

Since we don't have enough information to solve the equation, we need to find another equation. We know that Borya made more shots than Anton, so we can assume that y = x + 2.

Substituting this value into Equation 1:

2x + (x + 2) = 9

Simplifying the equation:

3x + 2 = 9

Subtracting 2 from both sides:

3x = 7

Dividing both sides by 3:

x = 7/3

Since we can't have a fraction of a shot, we need to round the value of x to the nearest whole number. Therefore, Anton made 2 shots.

Now we can find the value of y:

y = x + 2 = 2 + 2 = 4

So, Borya made 4 shots.

Answer

Therefore, Borya made the basketball shot 4 times, and Anton made the basketball shot 2 times.