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

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)   (Show Source): You can put this solution on YOUR website!
.

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)   (Show Source): You can put this solution on YOUR website!
(1)
(2)
(3)
----------------------------
Plug (1) into (2)
(2)
(2)
Plug (3) into )2)
(2)
(2)
(2)
(2)
and
(3)
(3)
and
(1)
(1)
---------------------------
Diana sent 10
Miguel sent 72
Henry sent 18
---------------------------
check:
(2)
(2)
(2)
OK

Answer by greenestamps(13200)   (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.
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