Question

На балу 294 человека станцевали польку, галоп и мазурку. Каждый танцевал только один танец. Польку и галоп станцевали 210 человек, галоп и мазурку - 196. Сколько станцевало польку? Сколько галоп? Сколько мазурку?помогите!!!!

Answer 1

1) (210 + 196) - 294 = 112 (чел) - танцевали галоп

2) 210 - 112 = 98 (чел) - танцевали польку

3) 196 - 112 = 84 (чел) - танцевали мазурку

проверяем:

112 + 98 + 84 =  294

Answer 2

294-210=84(чел.)-станцевали польку.

210-196=14(чел.)-станцевали мазурку.

Answer 3

Analysis and Solution

To solve this problem, we need to determine the number of people who danced the polka, the galop, and the mazurka. We are given the following information:

- The total number of people who danced the polka, the galop, and the mazurka is 294. - 210 people danced the polka and the galop. - 196 people danced the galop and the mazurka.

Let's denote the number of people who danced the polka as P, the number of people who danced the galop as G, and the number of people who danced the mazurka as M.

From the given information, we can write the following equations:

1. P + G + M = 294 (equation 1) 2. P + G = 210 (equation 2) 3. G + M = 196 (equation 3)

To solve these equations, we can use a method called substitution. We'll solve equation 2 for P and substitute it into equations 1 and 3.

Solution

From equation 2, we have P = 210 - G.

Substituting P = 210 - G into equations 1 and 3, we get:

(210 - G) + G + M = 294 (equation 1) G + M = 196 (equation 3)

Simplifying equation 1, we have:

210 - G + M = 294 M - G = 84 (equation 4)

Now we have two equations:

M - G = 84 (equation 4) G + M = 196 (equation 3)

Adding equations 4 and 3, we get:

2M = 280

Dividing both sides by 2, we find:

M = 140

Substituting M = 140 into equation 3, we get:

G + 140 = 196

Subtracting 140 from both sides, we find:

G = 56

Finally, substituting G = 56 into equation 2, we find:

P + 56 = 210

Subtracting 56 from both sides, we find:

P = 154

Answer

Therefore, the number of people who danced the polka is 154, the number of people who danced the galop is 56, and the number of people who danced the mazurka is 140.