John has a board that is 6 feet long. He plans to use it to make 4 shelves. How long should each shelf be?

Question

the 4 shelves have lengths that are to be a series of consecutive even numbers.

Please show the work you did, because I'm extremely confused. thanks!

Answer 1

They have to be a series of consecutive even numbers... certainly it can't be the measurement in feet, because 2' + 4' = 6' and we would run out of lumber.

Do you mean in inches?

6 feet = 72 inches.

Let n be the first even number
Let n+2 be the next even number
Let n+4 be the next even number
Let n+6 be the next even number

All together this adds up to 72 inches:

n + (n + 2) + (n + 4) + (n + 6) = 72
4n + 12 = 72
4n = 60
n = 15

Clearly we have a problem with the question because 15 is *odd*, not even.

Best I can suggest is he make the boards be 14", 16", 18" and 20" for a total of 68 inches (with 4 inches of waste).

Answer 2

Ok, wow...this is terrible.

First, let's change feet to inches, otherwise we'll just melt our brains.

6 feet * 12 inches/foot = 72 inches.

We know that these shelves need to be consecutive even numbers, right?

We'll solve this using some algebra and some logic.

The first shelf would be x inches long.

The next-longest shelf would be x+2 inches long, right? Since consecutive even numbers are 2 numbers apart?

The next would be 2 inches longer than that.
That's x + 2 + 2, or x + 4.

And the fourth one would be two inches longer than that
x + 6

So let's put all this together:
We have four shelves, each with the following lengths
x
x+2
x+4
x+6
totaling 72 inches.

If all those shelves put together are 72 inches long, we can do this:
x + x+2 + x+4 + x+6 = 72

Now, we'll simplify, by combining like terms.
4x + 12 = 72.

4x = 60

x = 15

Sorry, but it can't be done, at least not without having some left over.

You could have one shelf of 14, one of 16, one of 18, and one of 20 inches, which adds up to 68 inches, with 4 left over. But unless he wants them to be ODD-numbered lengths, this problem is unsolvable.

Answer 3

smallest shelf is x
x
x+2
x+4
x+6
if he has a six foot board and the values have to been even, do they have to be integer? if not.
let us try converting to inches.
x
x+2 inches
x+4 inches
x+6 inches
so 4x+12=72
4x=60
x=15 inches. Which violates the initial requirement of even numbers.
So let x be 14 inches and you can make shelves that are
14"
16"
18"
20"
for a total of 68" which is a more likely solution since you can not get 72" of cut board out of a 72" board.

Good Luck

Answer 4

6 ft = 72 inches

there are 4 shelves that need to have consecutive even number lengths:

2x, 2x+2, 2x+4, 2x+6

2x + 2x+2 + 2x+4 + 2x+6 = 8x + 12

72 = 8x + 12
60 = 8x
x = 7.5

15, 17,19,21

Answer 5

1.5 feet long or 1 1/2 feet long.

Answer 6

18 inches , geez

Answer 7

try combinations and you'll make it