SOLUTION: Debra, Brian, and Austin sent a total of 87 text messages over their cell phones during the weekend. Debra sent 7 fewer messages than Brian. Austin sent 2 times as many messages as

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Question 1181099: Debra, Brian, and Austin sent a total of 87 text messages over their cell phones during the weekend. Debra sent 7 fewer messages than Brian. Austin sent 2 times as many messages as Debra. How many messages did they each send?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52884)   (Show Source): You can put this solution on YOUR website!
.
Debra, Brian, and Austin sent a total of 87 text messages over their cell phones during the weekend.
Debra sent 7 fewer messages than Brian. Austin sent 2 times as many messages as Debra.
How many messages did they each send?
~~~~~~~~~~~ 

Let x be the number for Debra.


Write equation as you read the problem


    Debra + Brian + Austin = 87


      x   + (x+7) + 2x     = 87


Simplify and solve


            4x            = 87 - 7 = 80

             x                     = 80/4 = 20.


ANSWER.   Debra 20;  Brian 20+7 = 27;  Austin 2*20 = 40.

Solved.



Answer by greenestamps(13209)   (Show Source): You can put this solution on YOUR website!


Take a few moments to figure out how to use the given information to set the problem up using a single variable. That will make the algebra to solve the problem less complicated.

The given information compares the numbers of messages from both Austin and Brian to the number sent by Debra. So use the number Debra sent for the variable.

x = number Debra sent
2x = number Austin sent (twice as many as Debra)
x+7 = number sent by Brian (because the number Debra sent was 7 less than the number sent by Brian)

The total number of messages was 87:






ANSWERS:
Debra: x = 20
Austin: 2x = 40
Brian: x+7 = 27
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