Question

Трем победителям соревнований по большому теннису присуждены денежные премии общей суммой 15 млн. руб. При этом вторая премия составила 60% первой и относительно к третьей как 1: 2/3. Каковы размеры этих премий?

Answer 1

первая премия х

вторая премия 0,6х

третья премия 0.6х*2/3=0,4х

составим уравнение

х+0,6х+0,4х=15000000

2х=15000000

х=15000000:2

х=7500000 первая премия

7500000*0,6=4500000 вторая премия

7500000*0,4=3000000 третья премия

=====================================

Answer 2

Calculation of Prize Sizes

To determine the sizes of the three prizes awarded to the winners of the tennis competition, we can use the given information. Let's denote the first prize as P1, the second prize as P2, and the third prize as P3.

According to the information provided, the second prize is 60% of the first prize, and the third prize is in a ratio of 1:2/3 relative to the second prize.

Let's calculate the sizes of the prizes step by step:

1. We know that the second prize (P2) is 60% of the first prize (P1). Therefore, we can write the equation: P2 = 0.6 * P1.

2. The third prize (P3) is in a ratio of 1:2/3 relative to the second prize (P2). This means that P3 is equal to P2 multiplied by 2/3. So, we can write the equation: P3 = (2/3) * P2.

3. The sum of the three prizes is given as 15 million rubles. Therefore, we can write the equation: P1 + P2 + P3 = 15,000,000.

Now, let's solve these equations to find the sizes of the prizes.

Solution:

Substituting the value of P2 from the first equation into the second equation, we get:

P3 = (2/3) * (0.6 * P1).

Substituting the values of P2 and P3 into the third equation, we get:

P1 + 0.6 * P1 + (2/3) * (0.6 * P1) = 15,000,000.

Simplifying the equation, we have:

P1 + 0.6 * P1 + (2/3) * 0.6 * P1 = 15,000,000.

Combining like terms, we get:

P1 * (1 + 0.6 + (2/3) * 0.6) = 15,000,000.

Simplifying further, we have:

P1 * (1 + 0.6 + 0.4) = 15,000,000.

P1 * 2 = 15,000,000.

Dividing both sides of the equation by 2, we get:

P1 = 7,500,000.

Now, we can substitute the value of P1 back into the first equation to find P2:

P2 = 0.6 * P1 = 0.6 * 7,500,000 = 4,500,000.

Finally, we can substitute the values of P1 and P2 into the second equation to find P3:

P3 = (2/3) * P2 = (2/3) * 4,500,000 = 3,000,000.

Answer:

Therefore, the sizes of the prizes are as follows: - The first prize (P1) is 7,500,000 rubles. - The second prize (P2) is 4,500,000 rubles. - The third prize (P3) is 3,000,000 rubles.

Please note that these calculations are based on the given information and the provided equations.