Question 1078289
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If a bottle and a glass balance with a pitcher, a bottle balances with a glass and a plate, and two pitchers balance with three plates, 
can you figure out how many glasses will balance with a bottle?
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Yes I can.


<pre>
Let b = mass of bottle;
    g = mass of glass;
    p = mass of pitcher;
    L = mass of plate.

Then from the condition, you have these 3 equations for 4 variables:

b + g = p,              (1)
b = g + L,              (2)
2p = 3L.                (3)


From (1) and (3) you have

b + g = {{{(3/2)*L}}}.          (4)


From (2) you have 

L = b - g.              (5)


Substitute (5) into (4) replacing and eliminating L. You will get

b + g = {{{(3/2)*(b-g)}}}.       (6)


Simplify (6):

2b + 2g = 3b - 3g  --->  5g = b.


<U>Answer</U>.  5 glasses balance 1 bottle.
</pre>

Solved.