Henry needs to rent a moving truck. Suppose Company A charges a rate of $50 per day and Company B charges $70 fee plus $30 per day. For what number of days is the cost the same?

##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.