The cost of transport is partly constant and partly varies as the distance covered. The cost is 1400 when 80 km is covered and 1600 when 130 km is covered. If the distance between 1 Korodn garage and Ketu Busstop is 16 km, find the cost of transportation.
Answer (2)
The cost of transportation for a distance of 16 km is calculated to be 1144. This total includes a fixed cost of 1080 and a variable cost of 4 per kilometer. Therefore, the transportation cost from Korodn garage to Ketu Busstop is 1144.
;
Define the cost equation: C = a + b × d , where C is the total cost, a is the constant cost, b is the variable cost per km, and d is the distance.
Set up a system of equations using the given data: 1400 = a + 80 b and 1600 = a + 130 b .
Solve the system of equations to find a = 1080 and b = 4 .
Calculate the cost for a 16 km distance: C = 1080 + 4 ( 16 ) = 1144 . The cost of transportation is 1144 .
Explanation
Understanding the Problem Let's break down this word problem step by step to make sure we understand it completely!
Setting up the Equation We're told the cost of transportation has two parts: a fixed cost (constant) and a variable cost that depends on the distance traveled. We can express this relationship with an equation. Let:
C = Total cost of transportation a = Constant (fixed) cost b = Variable cost per kilometer d = Distance covered in kilometers
Then, the equation is:
C = a + b × d
Forming the System of Equations We're given two scenarios:
When d = 80 km, $C = $1400. So, we have the equation:
1400 = a + 80 b
When d = 130 km, $C = $1600. So, we have the equation:
1600 = a + 130 b
Now we have a system of two equations with two unknowns ( a and b ).
Solving for Variable Cost We can solve this system of equations to find the values of a and b . Let's use the substitution or elimination method. Here, we'll use elimination. Subtract the first equation from the second:
( 1600 = a + 130 b ) − ( 1400 = a + 80 b )
This simplifies to:
200 = 50 b
Now, solve for b :
b = 50 200 = 4
So, the variable cost per kilometer is $4.
Solving for Constant Cost Now that we know b = 4 , we can substitute it back into either of the original equations to find a . Let's use the first equation:
1400 = a + 80 ( 4 ) 1400 = a + 320
Solve for a :
a = 1400 − 320 = 1080
So, the constant cost is $1080.
Calculating the Transportation Cost Now we know a = 1080 and b = 4 . We can write the complete cost equation:
C = 1080 + 4 d
We want to find the cost of transportation when the distance is 16 km. So, we substitute d = 16 into the equation:
C = 1080 + 4 ( 16 ) C = 1080 + 64 C = 1144
Therefore, the cost of transportation for 16 km is $1144.
Final Answer The cost of transportation between Korodn garage and Ketu Busstop, which are 16 km apart, is $1144.
Examples
Imagine you're running a delivery service. You have a fixed daily cost for your vehicle and insurance, plus a cost per kilometer for fuel and maintenance. This problem helps you calculate the total cost for a delivery based on the distance, ensuring you charge customers fairly and cover your expenses. Understanding these cost components is crucial for pricing your services effectively and making a profit. By analyzing fixed and variable costs, you can optimize your pricing strategy and remain competitive in the market.
