Use strings instead if you're going to bother with C++, really, because they have that == operator at the ready for use. Also, iostream.h makes your compiler look old. Dump that bad habit and use current stuff: you probably need a better compiler.
The user won't write out a number like that unless you tell them to.
Code:
// An improved version of the program! ^_^ Good mood...
#include <iostream>
#include <cctype>
#include <string>
#include <algorithm>
int main (void) {
std::string answer = "twenty";
std::cout << "How many apples did I buy? (word answers):";
std::cin >> answer;
// This dandy little algorithm transforms a string based on the
// predicate. I turned everything lower case to make sure it
// matches.
transform(answer.begin(), answer.end(), answer.begin(), ::tolower);
if(answer != "twenty")
{
std::cout << "Sorry, you're wrong\n";
}
else
{
std::cout << "Yes, that's correct\n";
}
return 0;
}