SOLUTION: Lisa, Boris, and Pablo sent a total of 113 text messages over their cell phones during the weekend. Pablo sent 5 fewer messages than Lisa. Boris sent 4 times as many messages as Pa

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Lisa, Boris, and Pablo sent a total of 113 text messages over their cell phones during the weekend. Pablo sent 5 fewer messages than Lisa. Boris sent 4 times as many messages as Pa      Log On


   

Question 1121701: Lisa, Boris, and Pablo sent a total of 113 text messages over their cell phones during the weekend. Pablo sent 5 fewer messages than Lisa. Boris sent 4 times as many messages as Pablo. How many messages did they each send?
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number Lisa sent
Let +b+ = number Boris sent
Let +c+ = number Pablo sent
————————————————-
(1) +a+%2B+b+%2B+c+=+113+
(2) +c+=+a+-+5+
(3) +b+=+4c+
———————————
There are 3 equations and 3 unknowns,
so it’s solvable
(3) +b+=+4%2A%28+a+-+5+%29+
And
(1) +a+%2B+4%2A%28+a+-+5+%29+%2B+a+-+5+=+113+
(1) +a+%2B+4a+-+20+%2B+a+-+5+=+113+
(1) +6a+-+25+=+113+
(1) +6a+=+138+
(1) +a+=+23+
And
(2) +c+=+23+-+5+
(2) +c+=+18+
And
(3) +b+=+4%2A18+
(3) +b+=+72+
———————————
Check:
(1) +23+%2B+72+%2B+18+=+113+
(1) +113+=+113+


Answer by ikleyn(52832) About Me  (Show Source):
You can put this solution on YOUR website!
.

This problem is intended to be solved using one equation and one unknown. 


Let L be the number of messages sent by Lisa.


Then Pablo sent (L-5) messages, while Boris sent 4*(L-5).


The equation is

    Lisa + Pablo + Boris   = 113,    or


    L    + (L-5) + 4*(L-5) = 113,


    L + L - 5 + 4L - 20    = 113


    6L = 113 + 5 + 20 = 138  ====>  L = 138%2F6 = 23.


Answer.  Lisa sent 23 messages, Pablo sent 23-5 = 18 messages  and Boris sent 4*18 = 72 messages.


Check.  23 + 18 + 72 = 113 messages.    ! Correct !

Solved.

---------------

If you want to see many other similar problems solved in this way, look into the lesson
    - More complicated word problems to solve using a single linear equation
in this site.