Question

Решите плиз задачу!! На турбазе имеются палатки и домики, вместе их 25. В каждом домике живут 4 человека, а в палатке 2 человека. Сколько на турбазе палаток и сколько домиков, если турбаза рассчитана на 70 человек?

Answer 1

X=25-15=10
4(25-y)+2y=70
100-4y+2y=70
2y=30
y=15

Answer 2

Problem Analysis

We are given that there are a total of 25 accommodations (tents and cabins) on a tourist base. Each cabin can accommodate 4 people, and each tent can accommodate 2 people. The tourist base is designed to accommodate a total of 70 people. We need to determine the number of tents and cabins on the tourist base.

Solution

Let's assume the number of cabins is C and the number of tents is T.

From the given information, we can form the following equations: 1. The total number of accommodations is 25: C + T = 25. 2. Each cabin accommodates 4 people: 4C. 3. Each tent accommodates 2 people: 2T. 4. The tourist base is designed to accommodate 70 people: 4C + 2T = 70.

We can solve these equations to find the values of C and T.

Solving the Equations

To solve the equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From equation 1, we have C = 25 - T.

Substituting this value of C into equation 4, we get: 4(25 - T) + 2T = 70.

Simplifying the equation: 100 - 4T + 2T = 70, -2T = -30, T = 15.

Substituting the value of T back into equation 1, we get: C + 15 = 25, C = 10.

Answer

Therefore, there are 10 cabins and 15 tents on the tourist base.

Verification

Let's verify our answer by checking if it satisfies all the given conditions.

1. The total number of accommodations is 25: 10 cabins + 15 tents = 25. This condition is satisfied. 2. Each cabin accommodates 4 people: 10 cabins * 4 people per cabin = 40 people. This condition is satisfied. 3. Each tent accommodates 2 people: 15 tents * 2 people per tent = 30 people. This condition is satisfied. 4. The tourist base is designed to accommodate 70 people: 40 people (from cabins) + 30 people (from tents) = 70 people. This condition is satisfied.

Therefore, our answer of 10 cabins and 15 tents satisfies all the given conditions.