How do you determine the amount of Linux system RAM in C++?

On Linux, you can use the function sysinfo which sets values in the following struct:

   #include <sys/sysinfo.h>

   int sysinfo(struct sysinfo *info);

   struct sysinfo {
       long uptime;             /* Seconds since boot */
       unsigned long loads[3];  /* 1, 5, and 15 minute load averages */
       unsigned long totalram;  /* Total usable main memory size */
       unsigned long freeram;   /* Available memory size */
       unsigned long sharedram; /* Amount of shared memory */
       unsigned long bufferram; /* Memory used by buffers */
       unsigned long totalswap; /* Total swap space size */
       unsigned long freeswap;  /* swap space still available */
       unsigned short procs;    /* Number of current processes */
       unsigned long totalhigh; /* Total high memory size */
       unsigned long freehigh;  /* Available high memory size */
       unsigned int mem_unit;   /* Memory unit size in bytes */
       char _f[20-2*sizeof(long)-sizeof(int)]; /* Padding for libc5 */
   };

If you want to do it solely using functions of C++ (I would stick to sysinfo), I recommend taking a C++ approach using std::ifstream and std::string:

unsigned long get_mem_total() {
    std::string token;
    std::ifstream file("/proc/meminfo");
    while(file >> token) {
        if(token == "MemTotal:") {
            unsigned long mem;
            if(file >> mem) {
                return mem;
            } else {
                return 0;
            }
        }
        // Ignore the rest of the line
        file.ignore(std::numeric_limits<std::streamsize>::max(), '\n');
    }
    return 0; // Nothing found
}

There isn't any need to use popen(). You can just read the file yourself.

Also, if their first line isn't what you're looking for, you'll fail, since head -n1 only reads the first line and then exits. I'm not sure why you're mixing C and C++ I/O like that; it's perfectly OK, but you should probably opt to go all C or all C++. I'd probably do it something like this:

int GetRamInKB(void)
{
    FILE *meminfo = fopen("/proc/meminfo", "r");
    if(meminfo == NULL)
        ... // handle error

    char line[256];
    while(fgets(line, sizeof(line), meminfo))
    {
        int ram;
        if(sscanf(line, "MemTotal: %d kB", &ram) == 1)
        {
            fclose(meminfo);
            return ram;
        }
    }

    // If we got here, then we couldn't find the proper line in the meminfo file:
    // do something appropriate like return an error code, throw an exception, etc.
    fclose(meminfo);
    return -1;
}

Remember /proc/meminfo is just a file. Open the file, read the first line, and close the file. Voilà!

Even top (from procps) parses /proc/meminfo. See here.