A bottle and drinking glass on the left side of a scale balance with a jug on the right side. The bottle alone balances the drinking glass and a plate. Three of these plates balance 2 of the jugs. How many of the glasses will balance a bottle?

Solution to the Problem: Let B represent a bottle, G a drinking glass, J a jug and P a plate. Let "=" represent being in balance. We are given the following: BG = J B = GP PPP = JJ Given: BG = J, add J to both sides to get: JBG = JJ Then: PPP = JBG Add 3 G's to both sides and replace J with BG to get: GPGPGP = GGGBGBG Now replace each GP with B to get: BBB = GGGGGBB Lastly, remove two B's from both sides to get: B = GGGGG Therefore five drinking glasses balance one bottle. Here is a more algebraic approach sent in by Ann Norman: let b stand for bottle, g stand for glass,and j stand for jug. b+g=j b=g+p 3p=2j b=j-g j-g=g+p j=2g+p 3p=2(2g+p) 3p=4g+2p p=4g p=b-g b-g=4g b=5g

Correctly solved by: