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