Question

В доме 320 квартир.Трёхкомнатных на 50 штук больше,чем однокомнатных, но на 70 штук меньше ,чем двухкомнатных.Сколько однокомнатных квартир в доме?

Answer 1

3к- х+50
2к- х+50+70
1к- х
х+50+х+50+70+х=320
3х=320-170
3х=150
х=150:3
х=50

Answer 2

Analysis and Solution

To solve this problem, we need to determine the number of one-bedroom apartments in a building with a total of 320 apartments. We are given the following information:

- The number of three-bedroom apartments is 50 more than the number of one-bedroom apartments. - The number of three-bedroom apartments is 70 less than the number of two-bedroom apartments.

Let's assign variables to represent the number of one-bedroom, two-bedroom, and three-bedroom apartments:

- Let x be the number of one-bedroom apartments. - Let y be the number of two-bedroom apartments. - Let z be the number of three-bedroom apartments.

Based on the given information, we can set up the following equations:

1. The total number of apartments is 320: - x + y + z = 320

2. The number of three-bedroom apartments is 50 more than the number of one-bedroom apartments: - z = x + 50

3. The number of three-bedroom apartments is 70 less than the number of two-bedroom apartments: - z = y - 70

To solve this system of equations, we can substitute equation 2 into equation 3:

x + 50 = y - 70

Now we have two equations with two variables:

x + y + z = 320 x + 50 = y - 70

Let's solve this system of equations to find the number of one-bedroom apartments (x).

Solution

To solve the system of equations, we can use the substitution method. Let's solve equation 2 for z:

z = x + 50

Substitute this expression for z in equation 1:

x + y + (x + 50) = 320

Combine like terms:

2x + y + 50 = 320

Rearrange the equation:

2x + y = 270

Now, let's solve equation 2 for y:

y = z + 70

Substitute this expression for y in equation 1:

x + (z + 70) + z = 320

Combine like terms:

x + 2z + 70 = 320

Rearrange the equation:

x + 2z = 250

Now we have a system of equations:

2x + y = 270 x + 2z = 250

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

From equation 2, we can solve for x:

x = 250 - 2z

Substitute this expression for x in equation 1:

2(250 - 2z) + y = 270

Distribute:

500 - 4z + y = 270

Rearrange the equation:

y - 4z = -230

Now we have two equations:

y - 4z = -230 x + 2z = 250

We can solve this system of equations using the method of elimination. Multiply the first equation by 2:

2y - 8z = -460

Add this equation to the second equation:

(2y - 8z) + (x + 2z) = -460 + 250

Simplify:

2y - 8z + x + 2z = -210

Combine like terms:

x + 2y - 6z = -210

Now we have one equation:

x + 2y - 6z = -210

To find the value of x, we need to know the values of y and z. Unfortunately, the problem does not provide this information. Therefore, we cannot determine the exact number of one-bedroom apartments in the building.

However, we can make some observations based on the equations:

- The number of three-bedroom apartments (z) is 50 more than the number of one-bedroom apartments (x). - The number of three-bedroom apartments (z) is 70 less than the number of two-bedroom apartments (y).

From these observations, we can conclude that the number of one-bedroom apartments (x) must be less than the number of three-bedroom apartments (z) and the number of two-bedroom apartments (y). However, without knowing the specific values of y and z, we cannot determine the exact number of one-bedroom apartments in the building.

In summary, we cannot determine the exact number of one-bedroom apartments in the building with the given information.