Question

there are 30 houses in the neighborhood. company x provides electricity to 1/3 of the houses. company y provides electricity to 2/5 of the houses. company z provides electricity to the remaining houses. how many houses does company z provide electricity to?

Explanation:

Step1: Find the fraction of remaining houses

Let the total number of houses be 1. Company X provides electricity to $\frac{1}{8}$ of the houses. So the fraction of remaining houses is $1-\frac{1}{8}=\frac{7}{8}$.

Step2: Find the fraction of houses Company Y serves among the remaining

Company Y provides electricity to $\frac{2}{5}$ of the remaining houses. So the number of houses Company Y serves is $\frac{2}{5}\times\frac{7}{8}=\frac{14}{40}=\frac{7}{20}$.

Step3: Find the fraction of houses Company Z serves

The fraction of houses Company Z serves is the remaining part after Company X and Company Y have served their portions. First, find the combined fraction of houses served by Company X and Company Y: $\frac{1}{8}+\frac{7}{20}=\frac{5 + 14}{40}=\frac{19}{40}$. Then the fraction of houses Company Z serves is $1-\frac{19}{40}=\frac{40 - 19}{40}=\frac{21}{40}$.

Answer:

$\frac{21}{40}$