Devon is going to make 3 shelves for her father. He has a piece of lumber 12 feet long. She wants the top shelf to be half a foot shorter than the middle shelf, and the bottom shelf to be half a foot shorter than twice the length of the top shelf. How long will each shelf be if she uses the entire 12 feet of wood?
If the top shelf has length x, then
x + (x + 1/2) + (2x - 1/2) = 12
Well, Devon certainly has her work cut out for her! Let's determine the length of each shelf step by step.
First, let's figure out the length of the middle shelf. We know that the top shelf is half a foot shorter, so the middle shelf must be 12 - 0.5 = 11.5 feet long.
Now, let's calculate the length of the top shelf. Since the top shelf is half a foot shorter than the middle shelf, it will be 11.5 - 0.5 = 11 feet long.
Lastly, we need to determine the length of the bottom shelf. It's half a foot shorter than twice the length of the top shelf. So, twice the length of the top shelf is 2 * 11 = 22 feet. Subtracting half a foot gives us the length of the bottom shelf: 22 - 0.5 = 21.5 feet.
To sum it up, the lengths of Devon's shelves will be:
- Top shelf: 11 feet
- Middle shelf: 11.5 feet
- Bottom shelf: 21.5 feet
Hope this helps! Happy shelf-making to Devon and her father!
Let's break down the problem step-by-step:
1. Let's start by determining the length of the top shelf. We can represent this length as "x" feet.
2. The middle shelf will be half a foot longer than the top shelf. Therefore, the length of the middle shelf will be "x + 0.5" feet.
3. The bottom shelf will be half a foot shorter than twice the length of the top shelf. Therefore, the length of the bottom shelf will be "2x - 0.5" feet.
4. Since Devon has a piece of lumber 12 feet long, the total length of all three shelves combined should add up to 12 feet.
So, we can set up the equation: x + (x + 0.5) + (2x - 0.5) = 12
5. Simplifying the equation, we get: 4x = 12
6. Dividing both sides of the equation by 4, we get: x = 3
Therefore, the length of the top shelf will be 3 feet, the length of the middle shelf will be 3 + 0.5 = 3.5 feet, and the length of the bottom shelf will be (2 * 3) - 0.5 = 5.5 feet.
To solve this problem, we need to set up an equation for each shelf and then solve for the unknowns.
Let's assume:
Length of the middle shelf = x feet
Length of the top shelf = x - 0.5 feet (since it is half a foot shorter than the middle shelf)
Length of the bottom shelf = 2 * (x - 0.5) - 0.5 feet (since it is half a foot shorter than twice the length of the top shelf)
Now, to find the value of x, we'll sum up the lengths of all three shelves, which should equal the total length of the lumber, i.e., 12 feet:
x + (x - 0.5) + (2 * (x - 0.5) - 0.5) = 12
Simplifying the equation:
x + x - 0.5 + 2x - 1 - 0.5 = 12
4x - 2 = 12
4x = 14
x = 14/4
x = 3.5
Now that we have the length of the middle shelf (x), we can calculate the lengths of the other shelves:
Length of the middle shelf = x = 3.5 feet
Length of the top shelf = x - 0.5 = 3.5 - 0.5 = 3 feet
Length of the bottom shelf = 2 * (x - 0.5) - 0.5 = 2 * (3.5 - 0.5) - 0.5 = 6.5 feet
Therefore, the lengths of the shelves Devon should make are:
Top shelf: 3 feet
Middle shelf: 3.5 feet
Bottom shelf: 6.5 feet