The cost of maintaining a car is partly constant and partly varies with the distance travelled in a given Month.The cost c for a particular month was 1250 when the distance travelled was 300km . In another month,the cost 35000 for a distance of 1200km .

Question

The cost of maintaining a car is partly constant and partly varies with the distance travelled in a given Month.The cost c for a particular month was 1250 when the distance travelled was 300km . In another month,the cost 35000 for a distance of 1200km .

Find:
a) The formula connection c and d
b) The cost of a jounery of 160km

Answer 1

I just want to get the formula connecting c and d👌

Answer 2

c = a+bd

Now you have
a+300b = 1250
a+1200b = 35000
Solve for a and b, then find a+160b

Answer 3

,solution

c=a+be
c=1250=a+b×300k
1250=a+300b..........................(1)
3500=a+1200b........................(2)

equation (2)-(1)
3500_1250=a-a+1200b-300b
2250=0+900b
2250=900b
divide both side by 900b
2250\900=900\900=2.5
find the formula connecting c & d

Answer 4

Substitute b=2.5 in equation 1 a+300(2.5) = 1250. a+750 = 1250. Collect like terms. a = 1250-750. a = 500.

Answer 5

Connecting formula = c = 500+2.5d

Answer 6

a) To find the formula connecting c (cost) and d (distance), we can use the information provided in two different scenarios:

Scenario 1:
Cost (c1) = $1250
Distance (d1) = 300km

Scenario 2:
Cost (c2) = $35000
Distance (d2) = 1200km

Since the cost is partly constant and partly varies with the distance traveled, we can assume that there is a fixed cost (fc) and a variable cost per kilometer (vc).

Let's form the equation based on these assumptions:
c = fc + (vc * d)

Now let's find the values of fc and vc using the information from the two scenarios:

From Scenario 1:
1250 = fc + (vc * 300)

From Scenario 2:
35000 = fc + (vc * 1200)

We now have a system of two equations with two unknowns (fc and vc). Solving this system will give us the values of fc and vc.

b) To find the cost of a journey of 160km, we can substitute the value of d (distance) into the formula we derived in part (a):

c = fc + (vc * d)

Substituting d = 160km:
c = fc + (vc * 160)

Using the values we found in part (a), substitute them into this formula to find the cost of the journey.

Answer 7

To find the formula connecting cost (c) and distance (d), we need to determine the constant and variable parts of the cost.

We are given two data points:
- In the first month, the cost was 1250 when the distance traveled was 300km.
- In another month, the cost was 35000 for a distance of 1200km.

Let's assume the constant part of the cost is represented by 'k' and the variable part of the cost is represented by 'v'.

From the first data point:
c = k + v * d
1250 = k + v * 300

From the second data point:
c = k + v * d
35000 = k + v * 1200

Now we have a system of two equations:

Equation 1: k + v * 300 = 1250
Equation 2: k + v * 1200 = 35000

To solve these equations, we can use the method of substitution. Rearrange Equation 1 to solve for k:
k = 1250 - v * 300

Substitute this value of k into Equation 2:
1250 - v * 300 + v * 1200 = 35000

Simplify the equation:
950 + v * 1200 = 35000

Rearrange the equation to solve for v:
v * 1200 = 35000 - 950
v * 1200 = 34050
v = 34050 / 1200
v = 28.375

Now substitute the value of v back into Equation 1 or 2 to solve for k. Let's use Equation 1:
k + 28.375 * 300 = 1250
k + 8512.5 = 1250
k = 1250 - 8512.5
k = -7262.5

Therefore, the formula connecting cost (c) and distance (d) is:
c = -7262.5 + 28.375 * d

To find the cost of a journey of 160km, substitute d = 160 into the formula:
c = -7262.5 + 28.375 * 160
c = -7262.5 + 4540
c ≈ 2737.5

So, the cost of a journey of 160km is approximately 2737.5.