Very simple word problem that Im overthinking...please help

The average house value in a neighborbood is $230,000 based on 100 houses. Due to some playground and street improvements, 50 houses have increased in value by $12,000 and the other 50 remained unchanged. What is the new average value of the 100 houses??

I know I am over thinking this, but I've been up all day and brain is shutting down, please help

Average value is $230000.
For some fifty houses the average value has been increased by $12000.
So, $230000+$12000 =$242000.
multiply this by 50
242000*50=12100000.
other fifty has the same 230000.
multiply 230000*50=11500000.
adding the first and second values and dividing by 100
236000

$236,000

50 houses increasing by $12,000 is equal to 100 houses increasing by $6000.

or long version -
50 houses remain @ 230,000 avg
Total value of 50 houses = (50 X 230,000 = $11,500,000)
50 houses now @ 242,000 avg
Total value of improved 50 houses = (50 x 242,000 = $12,100,000)

New avg = ($12.1M + $11.5M) / 100 = $236,000

$236,000

Since half of the houses increase in value, the average increases by half of the 12,000.
There are harder ways to calculate it, but this is one correct shortcut.

Original Value of 100 houses is $230,000*100 = 23,000,000
New Value = 23,000,000 + 50*12,000 = 23,600,000
New Average = 23,600,000/100 = $236,000

If half the houses have increased in value by $12,000 , then the mean increase would have to be half of that. The mean home price should rise 6,000 dollars.

(50x242,000 + 50x230,000)/100

236000$