i am supposed to solve this word problem using system of quatino methods
The annual cost of owning and opearting a car, C dollars, is a linear function of the distance, d kilometers, it is driven. C=md+b
the cost is $4600 for 10 000km and $9100 for 25 000km. Determien the values of m and b.
To solve this word problem using the system of equations method, we will create two equations using the given information, and then solve for the variables m and b.
Let's use the first piece of information: "The cost is $4600 for 10,000 km."
From this, we can form the equation:
C = md + b
4600 = 10000m + b ----(Equation 1)
Similarly, using the second piece of information: "The cost is $9100 for 25,000 km."
We can form the equation:
C = md + b
9100 = 25000m + b ----(Equation 2)
Now, we have a system of two equations with two variables (m and b):
Equation 1: 4600 = 10000m + b
Equation 2: 9100 = 25000m + b
To solve this system, we can use the method of substitution or elimination. Let's use substitution:
Let's solve Equation 1 for b:
b = 4600 - 10000m
Now substitute this value of b into Equation 2:
9100 = 25000m + (4600 - 10000m)
Simplify:
9100 = 25000m + 4600 - 10000m
Combine like terms:
9100 = 15000m + 4600
Subtract 4600 from both sides of the equation:
4500 = 15000m
Divide both sides of the equation by 15000:
m = 4500 / 15000
m = 0.3
Now substitute the value of m back into Equation 1 to solve for b:
4600 = 10000 (0.3) + b
Simplify:
4600 = 3000 + b
Subtract 3000 from both sides of the equation:
b = 1600
Thus, the values of m and b are:
m = 0.3
b = 1600
Therefore, the equation relating the cost C to the distance driven d is:
C = 0.3d + 1600.