Q:

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?

Accepted Solution

A:
Answer:The lengths of the shelves are 3.5 feet , 4.5 feet , 6 feetStep-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