SOLUTION: Teresa, Manuel, and Greg sent a total of 70 text messages over their cell phones during the weekend. Manuel sent 10 more messages than Teresa. Greg sent 3 times as many

Question 1090470: Teresa, Manuel, and Greg sent a total of
70
text messages over their cell phones during the weekend. Manuel sent
10
more messages than Teresa. Greg sent
3
times as many messages as Manuel. How many messages did they each send?
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

You could solve this by defining variables for the numbers of messages sent by each of the three. Then you could use the given information to set up a system of three equations in those three unknowns, and solve the system of equations.
But I think it is easier to read the question carefully so that you can solve the problem using only one variable.

Since the given information relates the numbers for both Greg and Teresa to the number for Manuel, probably the easiest choice for the variable is the number sent by Manuel. So

let x = number sent by Manuel

Then 3x = number sent by Greg (he sent 3 times as many as Manuel)

and x-10 = number sent by Teresa (the problem says Manuel sent 10 more than Teresa; so Teresa sent 10 fewer than Manuel)

The total number of messages is 70, so

I will assume you can finish the problem from there....
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