Question

in a development with 100 houses, 75% of the houses with aluminum siding have 3 or more bathrooms. if there are 12 houses with aluminum siding that have 2 or fewer bathrooms, how many houses in this development do not have aluminum siding?

Explanation:

Step1: Find the percentage of houses with aluminum siding that have 2 or fewer bathrooms

Since 75% of the houses with aluminum siding have 3 or more bathrooms, then \(100\% - 75\%=25\%\) of the houses with aluminum siding have 2 or fewer bathrooms.

Step2: Let the number of houses with aluminum siding be \(x\)

We know that 25% of \(x\) is 12. Mathematically, \(0.25x = 12\).

Step3: Solve for \(x\)

Divide both sides of the equation \(0.25x = 12\) by 0.25. So \(x=\frac{12}{0.25}=48\).

Step4: Find the number of houses without aluminum siding

The total number of houses is 100. If \(x = 48\) (number of houses with aluminum siding), then the number of houses without aluminum siding is \(100 - 48=52\).

Answer:

52