Solution to the Problem:
Here are the 10 Tallest Monuments:
Tallest monument:
A = 630'
Name = Gateway Arch
2nd Tallest monument:
B = 570'
Name = San Jacinto Monument
3rd Tallest monument:
C = 555'
Name = Washington Monument
4th Tallest monument:
D = 352'
Name = Perry's Victory and International Peace Memorial
5th Tallest monument:
E = 351'
Name = Jefferson Davis Memorial
6th Tallest monument:
F = 306'
Name = Bennington Battle Monument
7th Tallest monument:
G = 284'
Name = Soldiers and Sailors Monument
8th Tallest monument:
H = 252'
Name = Pilgrim Monument
9th Tallest monument:
J = 221'
Name = Bunker Hill Monument
10th Tallest monument:
K = 220'
Name = High Point Monument
Here is the algebra involved:
The 10 equations are:
(1) K = J - 1
(2) F + G = B + 20
(3) D = H + 100
(4) 25 (F - G) = C - 5
(5) K + J + D + H = 1045
(6) B = C + 15
(7) D = 2K - 88
(8) G + C = 3F - 79
(9) A = 3K - 30
(10) A + B + C + D + E + F + G + H + J + K = 3,741
Now group equations (1), (3), (5), (7), and (9) together to solve for D, H, J, K, and A.
Then group equations (2), (4), (6), and (8) together to solve for F, G, C, and B.
Finally, use equation (10) to solve for E.
D = 2J - 90 substitute (1) in (7)
J - 1 + J + D + D - 100 = 1045 substitute (1) and (3) in (5)
So these simplify to:
D - 2J = -90
2D + 2J = 1146
Adding, we obtain 3D = 1056,
so
D = 352.
Then, it follows that
H = 252.
2K = 352 + 88, so 2K = 440,
and
K = 220.
Then
J = 221.
F + G = C + 35 substitute (6) in (2) call it equation (11)
G - C = -F +35 Subtraction property of equality in (11), call it equation (12)
G + C = 3F - 79 equation (8)
2G + 44 = 2F add equations (12) + (8)
So, G + 22 = F call it equation (13)
25 (F - G) = C - 5 equation (4)
25F - 25G = C - 5 Distributive property
-F - G = -C - 35 Multiply (11) by -1
24F - 26G = -40F Add last two equations, call this equation (14)
12F - 13G = -20F Divide (14) by 2 and call it equation (15)
12 (G + 22) - 13G = -20 Substitute (13) in (15)
So, 12G +264 - 13G = -20
-G = -284, so
G = 284
It follows that
F = 306, B = 570, C = 555, and E = 351.