Four Shelves

harpazo

harpazo

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Harvey plans to use 5 ft of shelving for four shelves whose lengths are to be a series of consecutive even numbers. How many inches long should each shelf be? If x represents the length of the shortest shelf, which expression would represent the length of the longest shelf?

Solution

Let x = length of shortest shelf
Let x + 6 = length of longest shelf
Let 5 feet = 60 inches

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

Correct set up?
 
harpazo said:
x + x + 2 + x + 4 + x + 6 = 60

Correct set up?
Click to expand...
No. The shelf-lengths are consecutive Integers.

Here's an arbitrary example of four consecutive Integers:

44, 45, 46, 47

Now, if we were to let z = 44, then what expressions (using z) would represent the three numbers 45, 46, and 47?

How would you write the sum of all four expressions?

?
 
Yes, your set up is correct. Taking the length of the shortest shelf to be "x" since they "a series of consecutive even numbers" the other three have lengths x+ 2, x+ 4, and x+ 6. The total length is x+ x+ 2+ x+ 4+ x+ 6= 4x+ 12= 60.

4x= 60- 12= 48
x= 48/4= 12.

The four shelves have lengths 12, 14, 16, and 18 inches. The total length is 12+ 14+ 16+ 18= 60 inches which is, of course, 5 feet..
 
Otis said:
No. The shelf-lengths are consecutive Integers.

Here's an arbitrary example of four consecutive Integers:

44, 45, 46, 47

Now, if we were to let z = 44, then what expressions (using z) would represent the three numbers 45, 46, and 47?

How would you write the sum of all four expressions?

?
Click to expand...

Sorry Otis but my set up is correct.
 
harpazo said:
… my set up is correct.
Click to expand...
Yes. You were correct, and you still are. My previous post shows my goof (I missed the word "even" ):
Otis said:
… The shelf-lengths are consecutive Integers.
Click to expand...

I will spend the night in the corner (as soon as Jomo goes home). But first …

Rich (BB code): 
2020goofs := 2020goofs + 1
  …   …   …


< core update confirmed >​
​

\(\;\)
 
Otis said:
No. The shelf-lengths are consecutive Integers.
Click to expand...
The problem, as originally posted, said "consecutive even numbers".

Here's an arbitrary example of four consecutive Integers:

44, 45, 46, 47
Click to expand...
Four consecutive even integers would be 44, 46, 48, 60.

Now, if we were to let z = 44, then what expressions (using z) would represent the three numbers 45, 46, and 47?

How would you write the sum of all four expressions?

?
Click to expand...
 
Otis said:
Yes. You were correct, and you still are. My previous post shows my goof (I missed the word "even" ):


I will spend the night in the corner (as soon as Jomo goes home). But first …

Rich (BB code): 
2020goofs := 2020goofs + 1
  …   …   …


< core update confirmed >​
​

\(\;\)
Click to expand...

I figure you did not see the word EVEN in the original post.
 
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