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r - dplyr - mutate formula based on similarities in column names

I am trying to find a better way to run a mutate() on a combination of columns based on parts of the column names.

For example, a way to simplify the mutate function in the following code:

df <- data.frame(LIMITED_A = c(100,200),
                UNLIMITED_A = c(25000,50000),
                LIMITED_B = c(300,300),
                UNLIMITED_B = c(500,500),
                LIMITED_C = c(2,10),
                UNLIMITED_C = c(5,20))

df %>%
  mutate(FINAL_LIMITED = (LIMITED_A - LIMITED_B) / LIMITED_C,
         FINAL_UNLIMITED = (UNLIMITED_A - UNLIMITED_B) / UNLIMITED_C)

A formula with the form: (._A - ._B) / ._C and the result is given the name FINAL_.

Is there a way to simplify this to a single line of code in the mutate function?

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One idea is to convert the data frame to long format and conduct the calculation.

library(dplyr)
library(tidyr)

df2 <- df %>%
  mutate(ID = 1:n()) %>%
  gather(Type, Value, -ID) %>%
  separate(Type, into = c("Type", "Group")) %>%
  spread(Group, Value) %>%
  mutate(Final = (A - B)/C)
df2
  ID      Type     A   B  C Final
1  1   LIMITED   100 300  2  -100
2  1 UNLIMITED 25000 500  5  4900
3  2   LIMITED   200 300 10   -10
4  2 UNLIMITED 50000 500 20  2475

And you can always convert the data frame back to the wide format.

df3 <- df2 %>%
  gather(Group, Value, A:Final) %>%
  unite(Col, Type, Group) %>%
  spread(Col, Value) %>%
  select(colnames(df), 
         FINAL_LIMITED = LIMITED_Final, 
         FINAL_UNLIMITED = UNLIMITED_Final)
  LIMITED_A UNLIMITED_A LIMITED_B UNLIMITED_B LIMITED_C UNLIMITED_C FINAL_LIMITED FINAL_UNLIMITED
1       100       25000       300         500         2           5          -100            4900
2       200       50000       300         500        10          20           -10            2475

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