A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 5 tables is $43. The total cost to rent 8 chairs and 3 tables is $36. What is the cost to rent each chair and each table?
Mark the cost of chairs with C and the cost of tables with T.
The total cost to rent 2 chairs and 5 tables is $43 means:
2 C + 5 T = 43
The total cost to rent 8 chairs and 3 tables is $36 means:
8 C + 3 T = 36
Now you must solve system of two equqtions:
2 C + 5 T = 43
8 C + 3 T = 36
___________
Try to do that.
The solutions are:
C = 1.5 , T = 8
The cost to rent chair is $1.5
The cost to rent table is $8
Let's use a system of equations to solve this problem. Let's call the cost to rent a chair "c" and the cost to rent a table "t".
From the given information, we can write two equations:
2c + 5t = 43 (equation 1)
8c + 3t = 36 (equation 2)
To solve this system, we can use the method of elimination.
Multiply equation 1 by 3 and equation 2 by 5 to eliminate the t-term:
6c + 15t = 129 (equation 3)
40c + 15t = 180 (equation 4)
Now, subtract equation 3 from equation 4:
(40c + 15t) - (6c + 15t) = 180 - 129
40c + 15t - 6c - 15t = 51
34c = 51
c = 51/34
c = 1.50
Substitute the value of c into equation 1 to solve for t:
2(1.50) + 5t = 43
3 + 5t = 43
5t = 43 - 3
5t = 40
t = 40/5
t = 8
Therefore, the cost to rent each chair is $1.50, and the cost to rent each table is $8.
To find the cost to rent each chair and each table, we can set up a system of equations based on the given information.
Let's say the cost to rent each chair is C and the cost to rent each table is T.
From the first sentence, we can create the equation:
2C + 5T = 43
From the second sentence, we can create another equation:
8C + 3T = 36
Now we have a system of equations:
2C + 5T = 43 ...(Equation 1)
8C + 3T = 36 ...(Equation 2)
To solve this system of equations, we can use the method of substitution or elimination. Let's solve it using the method of substitution:
We rearrange Equation 1 to express C in terms of T:
2C = 43 - 5T
C = (43 - 5T)/2 ...(Equation 3)
Now we substitute Equation 3 into Equation 2:
8((43 - 5T)/2) + 3T = 36
By simplifying and solving this equation, we can determine the value of T, which represents the cost to rent each table.
Simplifying equation 2:
4(43 - 5T) + 6T = 36
172 - 20T + 6T = 36
172 - 14T = 36
-14T = 36 - 172
-14T = -136
T = -136 / -14
T = 9.714
The cost to rent each table is approximately $9.71.
Now, we can substitute the value of T back into Equation 3 to find the cost to rent each chair.
C = (43 - 5 * 9.714)/2
C = (43 - 48.57)/2
C = -5.571/2
C = -2.786
The cost to rent each chair is approximately -$2.79.
However, negative costs do not make sense in this context. It seems there might have been a mistake or inconsistency in the given information or calculations.
Please double-check the problem or provide additional information if possible.
2 c + 5 t = 43 ... 8 c + 20 t = 172
8 c + 3 t = 36
subtract the equations to eliminate c
... solve for t
... substitute back to find c