Brain Teasers
Ship Shape Shelves
The Fernandez family is making shelves to hang on wall brackets for the three kids' bedrooms. They bought a 4 foot by 8 foot sheet of plywood to cut into shelves 24 inches long by 8 inches deep. This would make the correct number of shelves, with no wood left over. They also bought some trim to edge the shelves. They are making Ricardo 3/4 as many shelves as they are making for Anthony. Corinthia is getting four more shelves than her brother Ricardo.
How many shelves are being made for each person?
How many shelves are being made for each person?
Answer
Anthony gets 8 shelves. Ricardo gets 6 shelves. Corinthia gets 10 shelves.From a 4 ft by 8 ft piece of plywood they could cut 24 shelves measuring 24 in. by 8 in. deep.
Let A = Anthony's number of shelves.
Then Ricardo's shelves are 3/4 times A and Corinthia's shelves are 3/4 times A plus four more.
A + (3/4 x A) + (3/4 x A) + 4 = 24
2.5A + 4 = 24 [combine like terms and convert fractions]
2.5A = 20 [subtract 4 from each side of the equation]
A = 8 [divide each side of the equation by 2.5]
Once you know the value of A (Anthony's number of shelves), you can find the answer for everybody else. So, Anthony gets 8 shelves, Ricardo gets 6, and Corinthia gets 10.
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