Heather, Eric and Bob sent a total of 82 text messages. Heather sent 6 fewer than Eric. Bob sent 2 times as many messages as Heather. How many messages did they each send?

Question

anonymous · Answer

Not sure how this qualifies as advanced algebra... or even how I keep messing up solving this >.<

anonymous · Answer

Lets say that Eric sent 'x' messages, then "6 fewer than Eric" means that Heather sent (x-6) messages. "Bob sent 2 times as many as Heather" means Bob sent 2(x-6) messages. Lets now add all these up and make it equal to 82:$$x+(x-6)+2(x-6) = 82 \Rightarrow 4x-18=82\Rightarrow 4x=100$$
Which gives x = 25.
So Eric sent 25 messages, Heather sent (25 - 6) = 19 messages, and Bob sent 2(25 - 6) = 38 messages

anonymous · Answer

Thank you very much.. I had an equation similar but just kept messin it up somewhere. Thanks again!