SOLUTION: I need more detail solution: A child has a bag full of little toy bricks each of dimensions 1cm x 1 cm x 1cm and decides to build a little wall with them. He wants to have 2 br

Question 824176: I need more detail solution:
A child has a bag full of little toy bricks each of dimensions 1cm x 1 cm x
1cm and decides to build a little wall with them. He wants to have 2 bricks in the top
row, 4 in the second row from the top, 6 in the third row from the top, and so on,
always placing two more bricks in every row below. If he has a total of 950 little
bricks, how tall can he make his wall?
Found 3 solutions by kjmugno, MathTherapy, milo1954:
Answer by kjmugno(4)   (Show Source): You can put this solution on YOUR website!
Lets use a chart. So, row 1 has 2 bricks;
r o w - 1
bricks- 2
total(bricks)- 2
the word problem also provides us with the following information;
r o w - 1 2 3
bricks- 2 4 6
total- 2 6 12
now that we have a graph, its easier to use a little algebra to figure out an equation;
for row to bricks, the equation would be row*2=bricks. for row to total, it would be row1*2=total row2*3=total row3*4=total row4*5=total. do you see the correlation?
now, we need to figure out how many rows contain 950 bricks. Lets input 950 into our bricks total equation...
rowX*X+1=950
do you follow?
lets solve for x....
my favorite way to do this in questions like this is the process of elimination, its much quicker.
so lets take a random number to use for x, lets say...15?
okay.
row15*16=950 ?
15*16=240, so thats not it. but now we know we need a much larger number. lets go for....25?
row25*26=950 ?
25*26=650
closer, but not quite it. we need a slighty larger number. lets go for 31?
row31*32=950 ?
31*32=992
well, we almost got it!! its barely too big, lets knock it down ONE row.
row30*31=950 ?
30*31=930, which is the closest we can get without exceeding our number of bricks.
with 950 bricks, in the order of rows specified, your wall can be 30 rows high.

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
I need more detail solution:
A child has a bag full of little toy bricks each of dimensions 1cm x 1 cm x
1cm and decides to build a little wall with them. He wants to have 2 bricks in the top
row, 4 in the second row from the top, 6 in the third row from the top, and so on,
always placing two more bricks in every row below. If he has a total of 950 little
bricks, how tall can he make his wall?

This is an arithmetic progression, with formula: .
Proceed to determine n, or number of rows, with:
being the sum of the AP, or 950
being the 1st term, or 2
d being the common difference, or 2
Plugging the variables into the formula should result in the quadratic equation:
This results in n, or number of rows being 30.822 ≈ 30
Since each brick is 1 cm high, then height of wall = 30 * 1, or cm
You can do the check!!
Send comments, �thank-yous,� and inquiries to �D� at MathMadEzy@aol.com.
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Answer by milo1954(10)   (Show Source): You can put this solution on YOUR website!
sequence 2,4,6,8....2n (n numbers of rows)

adding
(2+2n)n/2
let get approximate to 950
(2+2n)n/2=950
(2n + 2n^2)/2=950
n+n*n=950
for n=30
30+30*30=930
for n=31 rows
we need 31+31*31=992 blocks and we have only 950 so
30 rows tall is the answer

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