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

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(2825)   (Show Source):
You can put this solution on YOUR website!
You have the basic equations correct

So

}

And

Check for answers. Is the average of 2 and 12 = 7?

Answer by stanbon(57967)   (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(28715)   (Show Source):
You can put this solution on YOUR website!
Start with the second equation.

Multiply both sides by 2.

Multiply

Rearrange the equation

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Move onto the first equation

Plug in

Add

Multiply both sides by 2.

Multiply

Divide both sides by to isolate .

Reduce.

So one of the numbers is 2

Go back to the second equation

Plug in

Multiply

So the other number is 12