AIME I Problem 5 2007

[zefuri]

The formula for converting a Fahrenheit temperature F to the corresponding Celsius temperature C is C=(5/9)(F-32). An integer Fahrenheit temperature is converted to Celsius and rounded to the nearest integer; the resulting integer Celsius temperature is converted back to Fahrenheit and rounded to the nearest integer. For how many integer Fahrenheit temperatures T with 32 <= T <= 1000 does the original temperature equal the final temperature?

[stupidityismygam]

find all of the values mod 9 to see which ones follow the conditions of the problem...

after accomplishing that....find all of those values mod 9 in the range

the key is to COUNT CORRECTLY and dont miss it by 1...

if i remember correctly the answer is [unparseable or potentially dangerous latex formula]

[zefuri]

i think that should be write if i also remember correctly...i missed this one for the practice i took