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?

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