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Algebra Level 2

A bottle and a glass balances the jug. A bottle balances a plate and a glass. Two jugs balances 3 plates. From the given conditions, find out how many glasses will balance the bottle?

5 4 8 6

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1 solution

Ratul Pan
Mar 27, 2016

Let us denote the bottle by B B , jug by J J , plate by P P and glass by G G .
So from the first statement,
B + G = J . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 B~+~G~=~J................................\boxed{1}
From the second statement,
P + G = B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 P~+~G~=~B................................\boxed{2}
From the third statement,
3 P = 2 J 3P~=~2J
or, P = 2 3 J . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 P~=~\frac{2}{3}J....................................\boxed{3}
Putting value of \boxed{3}) in \boxed{2})
B = 2 3 J + G B~=~\frac{2}{3}J~+~G
or, 3 B = 2 J + 3 G 3B~=~2J~+~3G
or, 3 B = 2 B + 2 G + 3 G 3B~=~2B~+~2G~+~3G ....(putting value from 1 \boxed{1}
or, B = 5 G \boxed{B=5G}

I also did the same way. Nice solution

Ankit Kumar - 5 years, 2 months ago

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