The Eiffel Tower is 497 feet taller than the Washington monument. If each of the monuments were 58 feet shorter, the Eiffel Tower would be twice as tall as the Washington Monument. How tall is each? How do I set up an equation for this
E-497=W
E-58=2(W-58)
How do i find the hieght of each
To set up an equation for this problem, we need to define the heights of both the Eiffel Tower and the Washington Monument.
Let's say the height of the Eiffel Tower is ET and the height of the Washington Monument is WM.
According to the problem, the Eiffel Tower is 497 feet taller than the Washington Monument. We can write this as:
ET = WM + 497 -------- (Equation 1)
Now let's consider the second condition: if each monument were 58 feet shorter, the Eiffel Tower would be twice as tall as the Washington Monument. This means that the new height of the Eiffel Tower (when it's shortened by 58 feet) would be twice the height of the Washington Monument (when it's shortened by 58 feet).
So we have:
(ET - 58) = 2 * (WM - 58) -------- (Equation 2)
Now we have two equations, which we can solve to find the heights of the Eiffel Tower and the Washington Monument.
To solve this system of equations, we can use substitution or elimination. Let's use substitution. We can start by rearranging Equation 1 for WM:
WM = ET - 497
Now, substitute this expression for WM in Equation 2:
(ET - 58) = 2 * ((ET - 497) - 58)
Let's simplify this equation:
ET - 58 = 2 * (ET - 497 - 58)
ET - 58 = 2 * (ET - 555)
Next, distribute the 2 on the right side:
ET - 58 = 2ET - 1110
Combine like terms:
ET - 2ET = -1110 + 58
-ET = -1052
Finally, divide both sides by -1 to solve for ET:
ET = 1052
Now, substitute this value back into Equation 1 to find WM:
WM = ET - 497
WM = 1052 - 497
WM = 555
Therefore, the height of the Eiffel Tower (ET) is 1052 feet, and the height of the Washington Monument (WM) is 555 feet.