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.
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) (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