A rental company charges a flat fee of x dollars for a floor sander rental plus y dollars per hour of the rental. One customer rents a floor sander for 4 hours and pays $63. Another customer rents a floor sander for 6 hours and pays $87. Find the flat fee and the cost per hour for the rental and how much it would cost if someone wanted to rent a sander for 11 hours.
equation:
cost = yt + x, where t is the number of hours
case1:
4y + x = 63 ---> x = 63-4y
case2:
6y + x = 87 ---> x = 87-6y
so 63-4y = 87-6y
2y = 24
y = 12
back into 1st equation:
x = 63-4(12) = 15
cost equation:
cost = 12t + 15
so for 11 hrs
cost = 12(11)+15
= 147
why big brain
To solve this problem, we can set up a system of equations based on the given information.
Let's denote the flat fee as "a" dollars and the cost per hour as "b" dollars.
According to the first customer, who rented the sander for 4 hours and paid $63, we can write the equation:
4b + a = 63 (Equation 1)
According to the second customer, who rented the sander for 6 hours and paid $87, we can write the equation:
6b + a = 87 (Equation 2)
We can now solve this system of equations to find the values of "a" and "b".
First, let's subtract Equation 1 from Equation 2 to eliminate "a":
(6b + a) - (4b + a) = 87 - 63
2b = 24
b = 12
Substituting the value of "b" back into Equation 1:
4(12) + a = 63
48 + a = 63
a = 63 - 48
a = 15
Therefore, the flat fee of the sander rental is $15 and the cost per hour is $12.
To find out how much it would cost to rent the sander for 11 hours, we can substitute this value into one of the equations:
11b + a = ?
11(12) + 15 = 132 + 15 = $147
So, it would cost $147 to rent the sander for 11 hours.
To solve this problem, we can set up a system of equations based on the given information.
Let's assume that the flat fee for the rental is $a and the cost per hour is $b.
From the first customer's rental information, we can set up the equation:
4b + a = 63 ........(1)
From the second customer's rental information, we can set up another equation:
6b + a = 87 ........(2)
Now we can solve this system of equations to find the values of a and b.
First, we can multiply equation (1) by 6 and equation (2) by 4 to eliminate the coefficients of 'b' in both equations.
24b + 6a = 378 ........(3)
24b + 4a = 348 ........(4)
Now, subtract equation (4) from equation (3) to eliminate 'b':
(24b + 6a) - (24b + 4a) = 378 - 348
2a = 30
a = 15
Substitute the value of a back into equation (1) to find the value of b:
4b + 15 = 63
4b = 48
b = 12
So, the flat fee for the rental is $15, and the cost per hour is $12.
Now, let's calculate the cost if someone wants to rent a floor sander for 11 hours:
Using the cost per hour of $12, we can calculate the additional cost for 11 hours:
Additional cost = 12 * (11 - 4) = $84
Finally, we add the flat fee and the additional cost to get the total cost for 11 hours:
Total cost = 15 + 84 = $99.
Therefore, if someone wants to rent a sander for 11 hours, it would cost $99.