a party rental company is renting tables and chairs. the total cost to rent 2 chairs and 6 tables for $54. the total cost to rent 5 chairs and 3 tables is $36. how much per chair and table
2C + 6T = 54
5C + 3T = 36
Solve the two equations simultaneously for C and T, then check it to make sure you're right.
To find the cost per chair and table, we need to set up a system of equations based on the given information:
Let x be the cost per chair and y be the cost per table.
From the first statement, "the total cost to rent 2 chairs and 6 tables for $54," we can write the equation:
2x + 6y = 54
From the second statement, "the total cost to rent 5 chairs and 3 tables is $36," we can write the equation:
5x + 3y = 36
Now we can solve this system of equations using either substitution or elimination method. Let's use the elimination method.
Multiply the first equation by 3 and the second equation by 6 to eliminate the y term:
6x + 18y = 162
30x + 18y = 216
Now, subtract the first equation from the second equation:
(30x + 18y) - (6x + 18y) = 216 - 162
24x = 54
x = 54/24
x = $2.25
Substitute the value of x back into one of the original equations, let's use the first equation:
2($2.25) + 6y = 54
4.5 + 6y = 54
6y = 54 - 4.5
6y = 49.5
y = 49.5/6
y = $8.25
So, the cost per chair is $2.25, and the cost per table is $8.25.
To solve this problem, we need to set up a system of equations based on the given information.
First, let's assign variables to represent the cost per chair and table.
Let c be the cost per chair.
Let t be the cost per table.
According to the information provided, we can create two equations:
1) 2c + 6t = 54 (total cost to rent 2 chairs and 6 tables is $54)
2) 5c + 3t = 36 (total cost to rent 5 chairs and 3 tables is $36)
Now we can solve this system of equations using either substitution or elimination method.
Let's use the elimination method to eliminate one variable by manipulating the equations:
Multiply equation (1) by 5 and equation (2) by 2 to get:
10c + 30t = 270
10c + 6t = 72
Now, subtract the second equation from the first equation:
(10c + 30t) - (10c + 6t) = 270 - 72
24t = 198
t = 198/24
t = 8.25
We have found the cost per table: t = $8.25
Now we can substitute this value back into one of the original equations to find the cost per chair.
Let's use equation (1):
2c + 6(8.25) = 54
2c + 49.5 = 54
2c = 54 - 49.5
2c = 4.5
c = 4.5/2
c = 2.25
We have found the cost per chair: c = $2.25
Therefore, the cost per chair is $2.25 and the cost per table is $8.25.