SOLUTION: <pre>Eve has two more marbles than Solene. Solene has twice as many marbles as Steve. Steve has 7 less marbles than Eve. How many marbles do they have between them?</pre>

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: <pre>Eve has two more marbles than Solene. Solene has twice as many marbles as Steve. Steve has 7 less marbles than Eve. How many marbles do they have between them?</pre>      Log On


   



Question 37347:
Eve has two more marbles than Solene. 
Solene has twice as many marbles as Steve.
Steve has 7 less marbles than Eve. 
How many marbles do they have between them?

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
Eve has two more marbles than Solene. 
Solene has twice as many marbles as Steve.
Steve has 7 less marbles than Eve. 
How many marbles do they have between them?

Suppose Eve has x marbles, Solene has y marbles,
and Steve has z marbles.

>>...Eve has two more marbles than solene...<<

So Eve's marbles = Solene's marbles + 2 marbles, or

               x = y + 2 

>>...Solene has twice as many marbles as Steve...<<

So Solene's marbles = 2 times Steve's marbles, or

               y = 2z

>>...Steve has 7 less marbles than Eve...<<

So Steve's marbles = Eve's marbles - 7 marbles, or
                
               z = x - 7

So now you have the system of equations:

               x = y + 2
               y = 2z
               z = x - 7

Can you solve that system?  If not post again.

Answer to system:  (x, y, z) = (12, 10, 5)

However, the question was not "How many does each have?"
but:

>>...How many marbles do they have between them?...<<

So we add 12 + 10 + 5 and get 27 marbles between them.

Edwin
AnlytcPhil@aol.com