SOLUTION: The average of two numbers is 7. Find the numbers if three times one of the numbers is one half the other number. I tried using substitution from the two equations given, which I

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Question 196978: The average of two numbers is 7. Find the numbers if three times one of the numbers is one half the other number.
I tried using substitution from the two equations given, which I think are :
(x + y) / 2 = 7 and
3x = 1/2y
But I didn't have any luck

Found 3 solutions by vleith, stanbon, jim_thompson5910:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
You have the basic equations correct
%28x%2By%29%2F2+=+7+
x%2By+=+14
3x+=+y%2F2
6x+=+y
So
x%2By+=+14
x+%2B+6x+=+14}
7x+=+14
x+=+2
And 6%2A2+=+y
12+=+y
Check for answers. Is the average of 2 and 12 = 7?

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The average of two numbers is 7. Find the numbers if three times one of the numbers is one half the other number.
I tried using substitution from the two equations given, which I think are :
(x + y) / 2 = 7 and
3x = 1/2y
-----------------------
Those are good equations.
---
Rearrange to get:
x + y = 14
y = 6x
-------------
Substitute to solve for "x":
x + 6x = 14
x = 2 (one of the numbers)
y = 12 (the other number)
================================
Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3x+=+%281%2F2%29y Start with the second equation.


3x%282%29+=+y Multiply both sides by 2.


6x+=+y Multiply


y=6x Rearrange the equation


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


%28x+%2B+y%29+%2F+2+=+7+ Move onto the first equation


%28x+%2B+6x%29+%2F+2+=+7+ Plug in y=6x


%287x%29+%2F+2+=+7+ Add


7x+=+7%282%29+ Multiply both sides by 2.


7x+=+14+ Multiply


x=%2814%29%2F%287%29 Divide both sides by 7 to isolate x.


x=2 Reduce.


So one of the numbers is 2


y=6x Go back to the second equation


y=6%282%29 Plug in x=2


y=12 Multiply


So the other number is 12