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?

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Tony 24, Jane 19, and Keith 76.

Let's ole the reckon of messages sent by Tony ##t## Then Jane has sent ##(t-5)## (5 hither than Tony) And Keith has sent ##4( t - 5)##. (4 times as frequent 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 hither) and Keith 76 (indelicate times as frequent as Jane).

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

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