You are redecorating your bedroom and want to place two posters on the wall. Your wall is 12 feet, 6 inches long and each poster is 27 inches across. You want to make sure that the distance in between posters and the distance from each poster to the walls is equal. Your brother thinks you should place the posters about 30 inches from the wall. Is your brother's estimate reasonable?
To determine if your brother's estimate is reasonable, we need to calculate the total length occupied by the two posters with equal spacing in between and from the walls.
The length of the wall is given as 12 feet, 6 inches, which can be converted to inches as follows:
12 feet = 12 * 12 = 144 inches
6 inches = 6 inches
So, the total length of the wall is 144 + 6 = 150 inches.
Each poster is 27 inches across.
Considering equal spacing in between and from the walls, there will be 3 distances in total:
1. Distance from the left wall to the first poster
2. Distance between the two posters
3. Distance from the second poster to the right wall
If we let x be the distance in inches between the posters and from the posters to the walls, then the total length occupied by the posters and spacing can be expressed as:
27 + x + 27 + x + 27
= 81 + 2x
Since there are three distances total, the overall length of the wall covered by the posters and spacing can be expressed as:
3x + 81
For the wall to be fully covered, the overall length should be equal to the total length of the wall:
3x + 81 = 150
Simplifying the equation:
3x = 150 - 81
3x = 69
x = 69 / 3
x = 23
Therefore, the distance in between posters and from each poster to the walls should be 23 inches, not 30 inches as suggested by your brother.
In conclusion, your brother's estimate of 30 inches is not reasonable because it would result in a smaller overall length than the total length of the wall. Therefore, you should place the posters about 23 inches from the wall.