I have two questions...
1.Lenear system...If you are painting the white lines around the perimeter of a tennis court. You measure and find that the perimeter is 228ft and the lenght is 42ft longer that the width...I need to write a linear system equation where W will be the width of the tennis court and let L be the length of the tennis court....I need to find the length and width of the tennis court...I believe the equation maybe L=W + 42,,I'm loss...
2. A hotel rents a double occupanch room for $20 more than a single occupancy room. One night, the hotel took in $3115 after renting 15 double occupancy rooms and 26 single occupancy room. I need to write and solve a linear system equatio to find the cost of renting a double occupancy room and the cost of renting a single occupancy room...I don't know where to starte...please help...Thank you
1. Yes on the length, now write the perimeter equation 228=2L + 2W=2(W+42)+ 2W
1. To find the length and width of the tennis court, you can set up a linear system of equations based on the given information. Let's use W for the width and L for the length.
First, you are given that the perimeter of the tennis court is 228ft. The perimeter of a rectangle can be calculated by adding up the four sides.
Since there are two equal lengths and two equal widths in a rectangle, the formula for the perimeter can be written as:
Perimeter = 2L + 2W
Knowing that the perimeter is 228ft, you can write the equation:
2L + 2W = 228
Additionally, you are told that the length is 42ft longer than the width. This can be expressed as:
L = W + 42
Now, you have a system of two equations:
2L + 2W = 228
L = W + 42
To solve this system, you can substitute the second equation into the first equation. Replace L in the first equation with (W + 42):
2(W + 42) + 2W = 228
Simplify and solve for W:
2W + 84 + 2W = 228
4W + 84 = 228
4W = 228 - 84
4W = 144
W = 144/4
W = 36
Now that you know the width (W = 36), you can substitute this value back into the second equation to find the length:
L = W + 42
L = 36 + 42
L = 78
Therefore, the width of the tennis court is 36ft, and the length is 78ft.
2. To find the cost of renting a double occupancy room and the cost of renting a single occupancy room, you can again set up a linear system of equations based on the given information.
Let S represent the cost of a single occupancy room, and D represent the cost of a double occupancy room.
You are told that the hotel earned a total of $3115 after renting 15 double occupancy rooms and 26 single occupancy rooms. This can be expressed as:
15D + 26S = 3115
Additionally, you are informed that the cost of a double occupancy room is $20 more than the cost of a single occupancy room. This can be written as:
D = S + 20
Now, you have a system of two equations:
15D + 26S = 3115
D = S + 20
To solve this system, you can substitute the second equation into the first equation. Replace D in the first equation with (S + 20):
15(S + 20) + 26S = 3115
Simplify and solve for S:
15S + 300 + 26S = 3115
41S + 300 = 3115
41S = 3115 - 300
41S = 2815
S = 2815/41
S ≈ 68.66
Now that you know the cost of a single occupancy room (S ≈ 68.66), you can substitute this value back into the second equation to find the cost of a double occupancy room:
D = S + 20
D = 68.66 + 20
D ≈ 88.66
Therefore, the cost of renting a single occupancy room is approximately $68.66, and the cost of renting a double occupancy room is approximately $88.66.