##3.5## days

##3.5## days

Given:

##d = “rate”##
##”Company A”= 50d##
##”Company B”= 30d + 70##

Here, the problem is asking us to calculate the number of days after which the cost is the same. Thus, we have to equate both values.

##50d = 30d + 70##
##50d – 30d = 30d – 30d + 70##
##20d = 70##
##d = 3.5##

Now, to check the answer, plug it into the equations

##”Company A” = 50(3.5)##
##”Company A” = 175##
##”Company B” = 30(3.5) + 70##
##”Company B” = 105 + 70##
##”Company B” = 175##

Now we know both answers are equal.
Tips:
When starting to read this problem, think, how will these both get the same answer. The only way is to equate them.
Also, I went the long way.