SOLUTION: Two full juice boxes weigh as much as 18 grapes and one half-full juice box. An empty juice box weighs as much as 6 grapes. A full juice box then weighs as much as how many grapes?

Question 204760: Two full juice boxes weigh as much as 18 grapes and one half-full juice box. An empty juice box weighs as much as 6 grapes. A full juice box then weighs as much as how many grapes? How much does the contents of one juice box, without the box, weigh in grapes?

Answer by alicealc(293) (Show Source): You can put this solution on YOUR website!
weight of juice content DISABLED_event_only= J
weight of an empty juice box = E
weight of a grape = G

1st equation:
2J + 2E = 18G + 1/2 J + E
2J - 1/2 J - 18G + 2E - E = 0
4/2 J - 1/2 J - 18G + E = 0
3/2 J - 18G + E = 0

2nd equation:
E = 6G

substitute E = 6G into the 1st equation:
3/2 J - 18G + E = 0
3/2 J - 18G + 6G = 0
3/2 J - 12G = 0
3/2 J = 12G
J = 12G * 2/3 = 24/3 G = 8G

so, a full juice box equals with J + E = 8G + 6G = 14G = 14 grapes
the juice content only (without the box) equals with J = 8G = 8 grapes

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