Recalculate the new weighted mean when merging two

I'm working on a data frame that contains:

counts per cluster (flow cytometry data)
of several files
and mean, max, min, total for lots of variables recorded by the machine.

In the case that I want to reduce the number of groups (pool similar clusters together) I would want to merge all the information in a file for group 'a' and 'b' by file

So far, following this SO Question I have already worked out the min, max, and total, but am stuck on how to get the following calculation working in this structure (mutate_at) using a custom function which would do:

(counts of 'a' * mean of 'a' + counts of 'b' * mean of 'b') / sum(counts for 'a', counts of 'b' )

in order to recalculate the new mean for each of the mean_i columns, where "mean" in the equation refers to 1 of the columns containing mean values I'm calling with vars(mean_cols)

The code so far:

library(dplyr)

set.seed(123)
df <- data.frame(ID = 1:20, 
                 total_X = runif(20), 
                 min_X = runif(20),
                 max_X = runif(20),
                 mean_X = runif(20),
                 total_Y = runif(20), 
                 min_Y = runif(20),
                 max_Y = runif(20),
                 mean_Y = runif(20),
                 Counts = runif(20)*1000,
                 category = rep(letters[1:5], 4), 
                 file = as.factor(sort(rep(1:4, 5)))) 



total_cols = names(df)[which(grepl('total', names(df)))]
min_cols = names(df)[which(grepl('min', names(df)))]
max_cols = names(df)[which(grepl('max', names(df)))]
mean_cols = names(df)[which(grepl('total', names(df)))]

recalmean <- function() { sum(Counts * vars)/sum(Counts)}
  #counts of 'a'  * mean of 'a'  + counts of 'b'  * mean of 'b'  / sum(counts for 'a', counts of 'b' )

x <- df %>% bind_rows(
  df %>% 
    filter(category %in% c('a' , 'b')) %>%
    group_by(file) %>% 
    mutate_at(vars(total_cols), sum) %>%
    mutate_at(vars(min_cols), min) %>%
    mutate_at(vars(max_cols), max) %>%
    # mutate_at(vars(mean_cols), recalmean) %>%  ## this line needs to do the custom weighed mean calculation
    mutate(category = paste0(category,collapse='')) %>% 
    filter(row_number() == 1 & n() > 1)
) %>% mutate(ID = row_number())

got to admit it was challenging...you should reconsider the data structure

library(tidyverse)

set.seed(123)
df <- data.frame(ID = 1:20, 
                 total_X = runif(20), 
                 min_X = runif(20),
                 max_X = runif(20),
                 mean_X = runif(20),
                 total_Y = runif(20), 
                 min_Y = runif(20),
                 max_Y = runif(20),
                 mean_Y = runif(20),
                 Counts = runif(20)*1000,
                 category = rep(letters[1:5], 4), 
                 file = as.factor(sort(rep(1:4, 5)))) 


x <- df %>% bind_rows(
  gather(df,metric,value,-ID,-file,-category,-Counts) %>% 
    mutate(group=str_extract(metric,"[A-Z]$"),metric = str_replace(metric,"_.$","")) %>% 
    filter(category %in% c('a' , 'b')) %>% 
    spread(metric,value) %>% 
    group_by(file,group) %>% 
    summarise(Counts = mean(Counts),
              category = paste0(category,collapse = ''),
              max = max(max),
              min = min(min),
              total = sum(total),
              mean = sum(Counts * mean)/sum(Counts)) %>% 
    ungroup() %>% 
    gather(metric,value,-file,-group,-category,-Counts) %>% 
    mutate(metric = paste(metric,group,sep='_'),group=NULL) %>% 
    spread(metric,value) %>% 
    mutate(ID=0)
) %>% mutate(ID = row_number())