Let R be the number of rented residences and O be the number of owned residences.

According to the given information, we have the ratio of rented to owned residences as 7:4:

R/O = 7/4

We are also given that there are 150 more rented residences than owned residences:

R = O + 150

Now, we can set up a system of equations to solve for R and O:

R/O = 7/4
R = O + 150
To eliminate R, we can use the second equation:

R = O + 150

Now, substitute this expression for R into the first equation:

(O + 150)/O = 7/4

Cross-multiply to solve for O:

4(O + 150) = 7O

4O + 600 = 7O

Subtract 4O from both sides:

600 = 3O

Now, divide by 3:

O = 600/3 O = 200

Now that we know the number of owned residences (O), we can find the number of rented residences (R) using the second equation:

R = O + 150 R = 200 + 150 R = 350

So, there are 200 owned residences and 350 rented residences in the town. To find the total number of residences, simply add these two numbers together:

Total = Owned + Rented Total = 200 + 350 Total = 550

Therefore, the total number of residences in the town is 550.