SOLUTION: Nicole, Ali, and Ryan sent a total of 68 text messages over their cell phones during the weekend. Ryan sent 3 times as many messages as Ali. Ali sent 7 more messages than Nicole.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Nicole, Ali, and Ryan sent a total of 68 text messages over their cell phones during the weekend. Ryan sent 3 times as many messages as Ali. Ali sent 7 more messages than Nicole.      Log On


   



Question 1125180: Nicole, Ali, and Ryan sent a total of 68 text messages over their cell phones during the weekend. Ryan sent 3
times as many messages as Ali. Ali sent 7 more messages than Nicole. How many messages did they each send?

Found 2 solutions by PRMath, josgarithmetic:
Answer by PRMath(133) About Me  (Show Source):
You can put this solution on YOUR website!
Nicole, Andy and Ryan sent 68 messages, so this means all of their messages added together equals 68.
Nicole + Andy + Ryan = 68 messages.


SO let's make variables for each name. I suggest:
N for Nicole
A for Andy
R for Ryan


Now lets break down what they tell us about each person:

Nicole: They give us no info so she made N calls

Ali: Sent 7 more messages than Nicole which is: A = N + 7

Ryan: Sent three times as many messages as Ali which: 3A

BUT... Ali is REALLY: A = N + 7
We can substitute A in for Ryan's calls which will give us:

3A
3(N + 7)


See how all the variables are "N" now?

SO we can say this:


N + N + 7 + 3(N + 7) = 68 Now we solve by distributing the 3...
N + N + 7 + 3N + 21 = 68 Now we add like terms
5N + 28 = 68 Now let's subtract 28 from both sides
5N = 40 Now let's divide both sides by 5
N = 8


SO! Nicole made 8 texts: N = 8


Ali is N + 7 which is:
8 + 7 = 15 (Ali made 15 texts) A = 15


Ryan has tree times as many texts as Ali, which is:
3(A) =
3(15) = 45



All together we have:
Nicole: 8 texts
Ali: 15 texts
Ryan: 45 texts


TOTAL: 68 texts


Does this make sense? I hope so.

Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
PERSON       NUMBER
Nicole         n
Ali            n+7
Ryan           3(n+7)
TOTAL          68

n%2B%28n%2B7%29%2B3%28n%2B7%29=68-------solve this, and then evaluate the expressions for Ali and Ryan.
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n%2Bn%2B7%2B3n%2B21=68
5n%2B28=68
5n=40
highlight_green%28n=8%29
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