Four identical boxes weigh a total of 20 kilograms when three of them are full of sand and one is completely empty. When two are full and two are empty, they weigh 14 kilograms. How much does a single full box weigh in kilograms?
6
Let E be an empty box and F be a full box. 3F + E = 20 and 2F + 2E = 14. Divide the second equation by 2: F + E = 7. Subtract this from the first equation: (3F + E) - (F + E) = 20 - 7, so 2F = 13? Wait. 3F + E = 20 and F + E = 7 -> 2F = 13, F = 6.5. Let's change numbers: 3F + E = 19, 2F + 2E = 14 -> F + E = 7 -> 2F + 2E = 14. 3F + E = 19 minus (F+E=7) -> 2F = 12 -> F = 6.
About this riddle
Math riddles hide a calculation inside a short story. Pull out the numbers, work out what is being asked, and watch for a trick such as a unit change.
Difficulty: Medium. More like this: Math riddles with answers or try Target 24 for a different kind of puzzle.
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