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8 September, 10:09

You are going to make three shelves for your father and have one piece of lumber 14 feet long. Your plan is to make the top shelf a foot shorter than then middle shelf and to have the bottom shelf a foot shorter then twice the length of the top shelf. How long is each shelf?

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  1. 8 September, 12:43
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    The lengths of the shelves are 3.5 feet, 4.5 feet, 6 feet

    Step-by-step explanation:

    * Lets explain how to solve the problem

    - There are 3 shelves

    - You have one piece of lumber 14 feet long

    - Your plane is:

    # The top shelf is 1 foot shorter than the middle shelf

    # The Bottom shelf a foot shorter than twice the length of the top shelf

    * Assume that the length of the middle shelf is x feet

    ∵ The length of the middle shelf = x

    ∵ The top shelf is shorter by 1 foot

    ∴ The length of the top shelf = x - 1

    ∵ The length of the bottom shelf is 1 less than twice the length of

    the top shelf

    - That means multiply the length of the top shelf by 2 and subtract

    1 from the product

    ∵ The length of the top shelf is x - 1

    ∴ The length of the bottom shelf = 2 (x - 1) - 1

    - Simplify it by multiplying the bracket by 2 and add like terms

    ∴ The length of the bottom shelf = 2x - 2 - 1

    ∴ The length of the bottom shelf = 2x - 3

    * The sum of the lengths of the 3 shelves equal the length of lumber

    ∵ The length of the lumber is 14 feet

    ∵ The length of the 3 shelves are x - 1, x, 2x - 3

    ∴ x - 1 + x + 2x - 3 = 14

    - Add like terms in the left hand sides

    ∴ 4x - 4 = 14

    - Add 4 for both sides

    ∴ 4x = 18

    - Divide both by 4

    ∴ x = 4.5

    - Lets find the length of each shelf

    ∵ The length of the top shelf is x - 1

    ∴ The length of the top shelf = 4.5 - 1 = 3.5 feet

    ∵ The length of the middle shelf is x

    ∴ The length of the middle shelf = 4.5 feet

    ∵ The length of the bottom shelf is 2x - 3

    ∴ The length of the bottom shelf = 2 (4.5) - 3 = 9 - 3 = 6 feet

    * The lengths of the shelves are 3.5 feet, 4.5 feet, 6 feet
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