A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 2 tables is $18. The total cost to rent 3 chairs and 8 tables is $55. What is the cost to rent each chair and each table ?
5 c + 2 t = 18
3 c + 8 t = 55
multiply first eqn by 4
20c + 8 t = 72
3 c + 8 t = 55
------------------------- subtract
17 c = 17
c = $ 1.00
etc
To find the cost of renting each chair and each table, we can set up a system of equations based on the given information.
Let's assume the cost of renting one chair is 'c' dollars and the cost of renting one table is 't' dollars.
Based on the given information, we can create the following equations:
Equation 1: 5c + 2t = 18 (Total cost to rent 5 chairs and 2 tables is $18)
Equation 2: 3c + 8t = 55 (Total cost to rent 3 chairs and 8 tables is $55)
Now, we can solve this system of equations to find the values of 'c' and 't'.
We can start by multiplying Equation 1 by 3 and Equation 2 by 5 to eliminate the variable 'c':
3(5c + 2t) = 3(18)
5(3d + 8t) = 5(55)
Simplifying:
15c + 6t = 54
15c + 40t = 275
Next, subtracting Equation 1 from Equation 2:
15c + 40t - (15c + 6t) = 275 - 54
Simplifying:
34t = 221
Dividing both sides by 34:
t = 221/34 ≈ 6.5
Now, we can substitute the value of 't' into either Equation 1 or Equation 2 to find the value of 'c'. Let's use Equation 1:
5c + 2(6.5) = 18
5c + 13 = 18
Subtracting 13 from both sides:
5c = 5
Dividing both sides by 5:
c = 1
Therefore, the cost to rent each chair is $1 and the cost to rent each table is $6.5 (approximately).
So, the cost to rent each chair is $1 and the cost to rent each table is $6.5.
5c + 2t = 18
3c + 8t = 55
Multiply first equation by 4, then subtract second equation from the first.
You should be able to take it from there.