Length of Each Shelf

[harpazo]

John has a board that is 5 feet long. He plans to use it to make 4 shelves whose lengths are to be a series of consecutive even numbers. How long should each shelf be (in inches)?

Solution:

The consecutive integers are x, x + 2 and x + 4, and x + 6. I noticed that we use the same set up here as when searching for odd consecutive integers. Why?

I know that 5 feet is 60 inches.

So, the correct equation is

x + x + 2 + x + 4 + x + 6 = 60

4x + 12 = 60

4x = 60 - 12

4x = 48

x = 48/4

x = 12

The 4 consecutive even integers, in terms of inches, are 12 inches, 14 inches, 16 inches, 18 inches.

 

[Dr.Peterson]

This problem is poorly stated! My first thought was, how can 4 consecutive even numbers add up to 5? I only saw the mention of inches at the very end; the second sentence should have said, "... whose lengths (in inches) ...".

Whether we have consecutive even numbers or consecutive odd numbers, we find them by counting by 2. In this case, if x is even, the next even number is x+2; the same would be said if they were consecutive odd numbers, but this is not that problem.

Good work on solving it. (Of course, at the end you checked that 12+14+16+18 = 60.)

 

[harpazo]

This problem is poorly stated! My first thought was, how can 4 consecutive even numbers add up to 5? I only saw the mention of inches at the very end; the second sentence should have said, "... whose lengths (in inches) ...".

Whether we have consecutive even numbers or consecutive odd numbers, we find them by counting by 2. In this case, if x is even, the next even number is x+2; the same would be said if they were consecutive odd numbers, but this is not that problem.

Good work on solving it. (Of course, at the end you checked that 12+14+16+18 = 60.)

Of course, these are pretty easy problems. I will post weekly word problems that will increase in complexity.

 

[Romsek]

This problem is poorly stated! My first thought was, how can 4 consecutive even numbers add up to 5? I only saw the mention of inches at the very end; the second sentence should have said, "... whose lengths (in inches) ...".

I would say that this was written this way on purpose to see if the student (or their online tutor) is paying attention.

 

[harpazo]

I would say that this was written this way on purpose to see if the student (or their online tutor) is paying attention.

I found this question online. I have a book of algebra word problems but it is a lot easier to simply copy and paste similar questions found online. I show my work or partial work if the question makes no sense to me at all.

 

[Otis]

… we use the same set up here as when searching for odd consecutive integers. Why? …

Hi. It's because consecutive odd Integers and consecutive even Integers are each spaced two units apart. In other words, the expressions x, x+2, x+4, x+6 can represent either consecutive odd Integers or consecutive even Integers; the value of the first number in the list (x) determines which.

?

 

[harpazo]

Hi. It's because consecutive odd Integers and consecutive even Integers are each spaced two units apart. In other words, the expressions x, x+2, x+4, x+6 can represent either consecutive odd Integers or consecutive even Integers; the value of the first number in the list (x) determines which.

?

Interesting. I did not know this information.