Jane, Tony, and Keith sent a total of 119 text messages over their cell phones during the weekend. Jane sent 5 fewer messages than Tony. Keith sent 4 times as many messages as Jane. How many messages did they each send?

Tony 24, Jane 19, and Keith 76.

Let’s call the number of messages sent by Tony ##t## Then Jane has sent ##(t-5)## (5 less than Tony) And Keith has sent ##4( t – 5)##. (4 times as many as Jane)

Altogether they sent 119 texts, so we can write:

##t + ( t- 5 )+ 4( t – 5) = 119##

Expanding and simplifying we get

##t + t – 5 + 4t – 20 = 119##

##6t – 25 = 119##

##6t = 144##

##t = 24##

So Tony has sent 24 texts, Jane 19 (five less) and Keith 76 (four times as many as Jane).

Check ## 24 + 19 + 76 = 119##