Question

На теплоходе есть одноместные,двухместные и трёхместные каюты,всего кают 108. В путешествие на этом теплоходе отправились 240 пассажиров,свободных мест не осталось.Известно что трёхместных кают в три раза больше чем одноместных.Найдите сколько кают каждого типа на теплоходе.

Answer 1

Пусть 1-местных кают х, а 2-местных у, тогда 3-местных 3х.
Кают всего: x+y+3x=4x+y=108
А мест: x+2y+3*3x=10x+2y=240
Получаем систему
4x+y=108
5x+y=120
Вычитаем из 2 ур-ния 1 ур-ние.
x=12; отсюда 3x=36; y=108-12-36=60
Ответ: 1) 12; 2) 60; 3) 36.

Answer 2

Calculation of Cabin Types on the Cruise Ship

To find out the number of cabins of each type on the cruise ship, let's assign variables to represent the number of one-person cabins, two-person cabins, and three-person cabins.

Let: - x = number of one-person cabins - y = number of two-person cabins - z = number of three-person cabins

According to the given information: - The total number of cabins is 108: x + y + z = 108. - The total number of passengers is 240, and there are no vacant cabins: x + 2y + 3z = 240. - The number of three-person cabins is three times the number of one-person cabins: z = 3x.

We can now solve this system of equations to find the values of x, y, and z.

Solving the System of Equations

Substituting z = 3x into the first equation, we get: x + y + 3x = 108 4x + y = 108

Substituting z = 3x into the second equation, we get: x + 2y + 3(3x) = 240 x + 2y + 9x = 240 10x + 2y = 240

Now we have a system of two equations with two variables: 4x + y = 108 10x + 2y = 240

We can solve this system of equations using any method, such as substitution or elimination. Let's use the elimination method.

Multiplying the first equation by 2, we get: 8x + 2y = 216

Subtracting the second equation from this new equation, we eliminate y: (8x + 2y) - (10x + 2y) = 216 - 240 -2x = -24 x = 12

Substituting the value of x back into the first equation, we can solve for y: 4(12) + y = 108 48 + y = 108 y = 60

Finally, substituting the values of x and y back into the equation z = 3x, we can solve for z: z = 3(12) z = 36

Answer

Therefore, there are 12 one-person cabins, 60 two-person cabins, and 36 three-person cabins on the cruise ship.