SOLUTION: Raina, Kevin, and Dan sent a total of 104 text messages during the weekend. Dan sent 2 times as many messages as Raina. Kevin sent 8 more messages than Raina. How many

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Question 1161079: Raina, Kevin, and Dan sent a total of
104
text messages during the weekend. Dan sent
2
times as many messages as Raina. Kevin sent
8
more messages than Raina. How many messages did they each send?

Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Raina, Kevin, and Dan sent a total of 104 text messages during the weekend.
r + k + d = 104
Dan sent 2 times as many messages as Raina.
d - 2r
Kevin sent 8 more messages than Raina.
k = r + 8
Using the first equation, replace d with 2r; replace k with (r+8)
r + 2r + (r+8) = 104
4r = 104 - 8
r = 96/4
r = 24 msg by Raina
then
d = 2(24)
d = 48 msg by Dan
and
k = 24 + 8
k = 32 msg by Kevin
:
:
See if that checks out
24 + 48 + 32 = 104

Answer by greenestamps(13203) (Show Source):
You can put this solution on YOUR website!

The solution by the other tutor is fine....

But solving a problem like this is nearly always much easier if you take the time to set it up to be solved using a single variable instead of three.

The given information compares the numbers of messages sent out by both Dan and Kevin to the number sent out by Raina. So let your variable be the number sent out by Raina:

x = number sent out by Raini
2x = number sent out by Dan (twice as many as Raina)
x+8 = number sent out by Kevin (8 more than Raina)

Then write a single equation in the single variable that says the total number of messages was 104:

Solving that single equation is basic algebra -- much easier than working with three equations and three unknowns.