In a certain town 25% families own a cell phone, 15% families own a scooter and 65% families own neither a cell phone nor a scooter. If 500 families own both a cell phone and a scooter, then what is the total number of families in the town ?

Question

imstuck · Answer

Right off this is weird to me because if we are talking about a whole town and the percentages of families who own cells, scooters, or neither, it should come up to 100% and it adds up to 105%.  Anyway, I did it like this, but Im not 100% sure it's correct (or should I say 105%? jk).  If 25% of the families own phones and 15% of the families own scooters and the number of families total with phones and scooters is 500, we need to find out what the total number of people in the town is, right?  Here is what they want, in words, then we will try to translate those words into an equation.  40% of the total families in the town (that's 25% + 15%) is equal to 500 families who own cell phones and scooters.  What we don't know is the total number of families in the town, so we will call that x.  An equation that puts those words together is .40x = 500 (that's "40% of the families in a town is equal to 500 families").  Divide 500 by .4 and you get 1250.  That seems reasonable to me.   I also think that 65% is supposed to be 60%, because when I do the math at 40% owning phones, and then do it at 60% not owning phones, the total number of families in the town comes out the same at 1250.  If you do it with 65%, you get the total number of families in town at 1153.846.  Are you sure you copied the percentages correctly?  Anyways, that is what I come up with when I do it with a total family percentage of 100% as opposed to 105%.  Any question, just ask!  I'm pretty sure I did this correctly!