Final answer:
The height of the observation deck of the Space Needle is found by setting up the equation 7x + 10 = 605, based on given information. Solving for x gives us the distance from the observation deck to the top, which is used to calculate the observation deck's height from ground level, resulting in 520 feet.
Step-by-step explanation:
The question involves solving a problem related to the height of different parts of the Space Needle in Seattle, Washington. To determine the height of the observation deck, we set up an equation based on the given information. Let the distance from the observation deck to the top of the Space Needle be represented by x feet. Then, given that the height from the ground level to the observation deck is 10 feet more than six times this distance, we express this as x + 6x + 10. With the total height of the Space Needle being 605 feet, we can set up the equation:
7x + 10 = 605.
By subtracting 10 from both sides, we obtain 7x = 595. Dividing both sides of the equation by 7 yields x ≈ 85. Therefore, the distance from the observation deck to the top is approximately 85 feet. To find the height of the observation deck from the ground level, we add the distance from the ground to the observation deck, which is six times the distance from the observation deck to the top plus 10 feet: (6 * 85) + 10, giving us 520 feet as the height of the observation deck.