There are 156 concrete blocks available to make a retaining wall. The bottom 3 rows have the same amount of blocks. the next 6 rows will each have 2 blocks fewer than the row below it. How many blocks are in each row?

How can I find the answer to this question using algebraic (I think that's a word) language?

Guest Jul 15, 2014

#1**+34 **

You would first write this problem as an equation. Let's use x as the variable:

3x + (x - 2) + (x - 4) + (x - 6) + (x - 8) + (x - 10) + (x - 12) = 156

Simplify the equation by combining like terms (the x's and constants):

3x + 6x - 42 = 156

9x - 42 = 156

Add 42 to both sides:

9x = 198

Divide by 9:

x = 22

Now x represents the number of blocks in the bottom 3 rows. For the next 6 rows, just subtract two blocks from the row below it.

For example, the fourth row (from the bottom up) would be (x - 2) = 20 blocks.

The 5th row would be (x - 4) = 18 rows, and so on and so forth:)

kitty<3
Jul 16, 2014

#1**+34 **

Best Answer

You would first write this problem as an equation. Let's use x as the variable:

3x + (x - 2) + (x - 4) + (x - 6) + (x - 8) + (x - 10) + (x - 12) = 156

Simplify the equation by combining like terms (the x's and constants):

3x + 6x - 42 = 156

9x - 42 = 156

Add 42 to both sides:

9x = 198

Divide by 9:

x = 22

Now x represents the number of blocks in the bottom 3 rows. For the next 6 rows, just subtract two blocks from the row below it.

For example, the fourth row (from the bottom up) would be (x - 2) = 20 blocks.

The 5th row would be (x - 4) = 18 rows, and so on and so forth:)

kitty<3
Jul 16, 2014

#2**+3 **

kitty i dint understand how did u form that equation!can u please explain ur answer to me much more nicely!

rosala
Jul 16, 2014

#3**+8 **

Ok, so kitty is writing out an algebraic equation to solve this word problem.

The problem said that there were the same amount of bricks in the bottom three rows. The number of bricks is represented by x.

So, 3x tells us how many bricks there are in the bottom 3 rows.

The next 6 rows will have 2 blocks few *than the one before it.*

So, the next row will have x-2 bricks, the next row will have x-4 bricks, the next will have x-6, then x-8, x-10, x-12

This is 6 rows so we stop there.

Now we know the total number of bricks used is 156, so we set all this equal to 156, and we get:

3x + (x - 2) + (x - 4) + (x - 6) + (x - 8) + (x - 10) + (x - 12) = 156

(then kitty solved for x, which is the number of bricks on the bottom 3 rows, and then you can figure out the number of bricks on the other rows from that answer)

Here's a picture so you can visualize it:

NinjaDevo
Jul 16, 2014

#4**0 **

Thanks Kitty and Ninja, that was a great explanation from both of you.

Plus

That is a fabulous pictue Ninja. I am really impressed. I think that you should add this one to your new learning posts thread.

Melody
Jul 16, 2014

#6**0 **

Excellent Ninja, you know you can just add what ever you want to.

I'm interested in what you add but you do not need my approval.

We need a big section for log questions. We get so many of those and it would be nice if we can eventually just send people off to a very similar question and then they can have a proper go at their own one themselves.

Melody
Jul 16, 2014