Of all the houses in a certain neighorhood, 80% have garages. Of those houses with garages, 60% have two car garages. If there are 56 houses with garages that are not two car garages, how many houses are there in the neighborhood?

Options

A. `93`
B. `117`
C. `156`
D. `175`

Answer

To solve the problem, we will follow these steps:

1. **Define the total number of houses**: Let the total number of houses in the neighborhood be \( x \).

2. **Calculate the number of houses with garages**: Since 80% of the houses have garages, the number of houses with garages can be calculated as:
\[ \text{Number of houses with garages} = 0.8x \]

3. **Determine the percentage of houses with two-car garages**: It is given that 60% of the houses with garages have two-car garages. Therefore, the number of houses with two-car garages is:
\[ \text{Number of houses with two-car garages} = 0.6 \times (0.8x) = 0.48x \]

4. **Calculate the percentage of houses with one-car garages**: The remaining houses with garages must have one-car garages. Since 60% have two-car garages, 40% must have one-car garages:
\[ \text{Number of houses with one-car garages} = 0.4 \times (0.8x) = 0.32x \]

5. **Set up the equation based on the given information**: We know that there are 56 houses with one-car garages. Therefore, we can set up the equation:
\[ 0.32x = 56 \]

6. **Solve for \( x \)**: To find the total number of houses, we divide both sides of the equation by 0.32:
\[ x = \frac{56}{0.32} \]

7. **Calculate the value of \( x \)**:
\[ x = 175 \]

Thus, the total number of houses in the neighborhood is \( \boxed{175} \).