Question

The Gardenview Hotel is seventeen less than twice the height of the Plaza Hotel. If their combined height is 361 feet, how tall is the Gardenview Hotel?​

Answer 1

Height of garden view hotel = 235 ft

Explanation:

let

height of the plaza = a

height of Garden view Hotel = 2a - 17

combined height = 361 ft

The combined height can be represented as follows:

a + (2a - 17) = 361

3a - 17 = 361

collect like terms

3a= 361 + 17

3a = 378

divide both sides by 3

3a/3 = 378/3

a = 378/3

a = 126 ft

Height of garden view hotel = 2 × 126 - 17

Height of garden view hotel = 2 × 126 - 17

Height of garden view hotel = 252 - 17

Height of garden view hotel = 235 ft

Answer 2

The height of Gardenview hotel is 38 feet.

Explanation:

To solve this problem let first suppose Garden View Hotel is "x" and the Plaza Hotel is "y" so the first equation as it says in the question will be 17x- 2y =0 and the second equation will be their combined height which is x+y =361 . Now let's solve both the equations simultaneously to get the height of GardenView Hotel.

`17_x - 2_(y) =0` (1)

`x + y = 361` (2)

Now multiply the second whole equation by 2 so that we can eliminate y from both the equations , after doing that the final equation is
`19x = 772` and if we calculate x from this we will get the height of gardenview hotel which is 38 feet.