SOLUTION: Diana, Miguel and Henry sent a total of 100 text messages over their cell phone during the weekend. Miguel sent 4 times as many messages as Henry. Henry sent 8 more messages than D

Algebra ->  Linear-equations -> SOLUTION: Diana, Miguel and Henry sent a total of 100 text messages over their cell phone during the weekend. Miguel sent 4 times as many messages as Henry. Henry sent 8 more messages than D      Log On


   

Question 1143995: Diana, Miguel and Henry sent a total of 100 text messages over their cell phone during the weekend. Miguel sent 4 times as many messages as Henry. Henry sent 8 more messages than Diana. How many messages did they each send.?
Found 3 solutions by ikleyn, josmiceli, greenestamps:
Answer by ikleyn(52781) About Me  (Show Source):
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.
If Diana sent x messages, then Henry sent (x+8) messages, while Miguel sent 4*(x+8) messages.


The equation for the total is


    x + (x+8) + 4*(x+8) = 100   messages.


Solve it on your own.


My partial answer, in order for you may check your solution, is x= 10: Diana sent 10 messages.


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +m+=+4h+
(2) +d+%2B+m+%2B+h+=+100+
(3) +h+=+d+%2B+8+
----------------------------
Plug (1) into (2)
(2) +d+%2B+4h+%2B+h+=+100+
(2) +d+%2B+5h+=+100+
Plug (3) into )2)
(2) +d+%2B+5%2A%28+d+%2B+8+%29+=+100+
(2) +d+%2B+5d+%2B+40+=+100+
(2) +6d+=+60+
(2) +d+=+10+
and
(3) +h+=+10+%2B+8+
(3) +h+=+18+
and
(1) +m+=+4%2A18+
(1) +m+=+72+
---------------------------
Diana sent 10
Miguel sent 72
Henry sent 18
---------------------------
check:
(2) +d+%2B+m+%2B+h+=+100+
(2) +10+%2B+72+%2B+18+=+100+
(2) +100+=+100+
OK

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1) Miguel sent 4 times as many messages as Henry.

So x = Henry; 4x = Miguel.

(2) Henry sent 8 more messages than Diana.

So x-8 = Diana.

(3) The total number of messages was 100:

x+(4x)+(x-8) = 100

Solve using basic algebra.