SOLUTION: Nick traveled out of the country for a month. He purchased a plan from his cell phone company that would allow him to send text messages to friends and family back home.​ Nic

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Question 1109201: Nick traveled out of the country for a month. He purchased a plan from his cell phone company that would allow him to send text messages to friends and family back home.​ Nick's telephone company charges $ 0.40 for a regular text message and $ 0.70 for a multimedia text messages. This month Nick was billed $ 106 and he sent total of 205 messages. How many regular text messages and multimedia text messages did he​ send?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of reg text messages
Let +b+ = number of multimedia text messages
----------------------------------------------------
(1) +a+%2B+b+=+205+
(2) +.4a+%2B+.7b+=+106+
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(2) +4a+%2B+7b+=+1060+
Multiply both sides of (1) by +4+
and subtract (1) from (2)
(2) +4a+%2B+7b+=+1060+
(1) +-4a+-+4b+=+-820+
----------------------------
+3b+=+240+
+b+=+80+
and
(1) +a+%2B+80+=+205+
(1) +a+=+125+
-----------------------
He sent 125 regular and
80 multimedia messages
----------------------------
check:
(2) +.4a+%2B+.7b+=+106+
(2) +.4%2A125+%2B+.7%2A80+=+106+
(2) +50+%2B+56+=+106+
(2) +106+=+106+
OK