Answer:
x = 4
Step-by-step explanation:
2(4x-12)=8
4x-12=4
4x=16
x=4
The garden view hotel is 235 feet tall
Step-by-step explanation:
The given is:
- The garden view hotel is seventeen less than twice the height of the plaza hotel
- Their combined height is 361 feet
We need to find the height of the garden view hotel
Assume that the height of garden view hotel is x feet and the height of the plaza hotel is y feet
∵ The height of the garden view hotel = x feet
∵ The height of the plaza hotel = y feet
∵ The height of the garden view hotel is 17 less than twice the
height of the plaza hotel
- That means x is less than 2 × y by 17, equate x by the difference
of 2 × y and 17
∴ x = 2y - 17 ⇒ (1)
∵ Their combined height = 361 feet
∴ x + y = 361
- Find y in terms of x by subtraction x from both sides
∴ y = 361 - x ⇒ (2)
Substitute y in equation (1) by equation (2)
∵ x = 2(361 - x) - 17
- Simplify the right hand side
∴ x = 722 - 2x - 17
- Add like terms
∴ x = 705 - 2x
- Add 2x to both sides
∴ 3x = 705
- Divide both sides by 3
∴ x = 235
The garden view hotel is 235 feet tall
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log
5
x
(
2
x
−
4)=3x+2
Answer:
30 miles
Step-by-step explanation:
Let d represent the distance to the island. The relation between time, speed, and distance is ...
time = distance/speed
so the total time for the round trip is ...
d/15 +d/10 = 5
Multiplying by 30, we get
2d +3d = 150
d = 150/5 = 30
The island was 30 miles from the harbor.
Let the first number = x
The second number would be x +1
3rd number = x +2
4th number = x +3
5th number = x+4
6th number = x+5
7th number = x +6
8th number = x +7
9th number = x+8
The sum is 279
Combine like terms in the 9 numbers to get: 9x + 36 = 279
Solve for x:
9x + 36 = 279
Subtract 36 from both sides:
9x = 243
Divide both sides by 9:
x =27
The first number is 27
The last number would be 27 + 8 = 35
The sum of the first and last would be 27 + 35 = 63
