Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Mr buchanan is contemplating which chauffeured car service to take to the airport. the first cost $26 upfront and $1 per kilometer. The second costs $4 plus $2 per kilometer. For a certain driving distance, the teo companies charge the same total fare. What is the total fare? What is the distance?

Solution:

Let "x" be the kilometers travelled

For, Mr buchanan, the first cost $26 upfront and $1 per kilometer

Therefore,

Cost : 26 + 1x eqn 1

The second costs $4 plus $2 per kilometer

Therefore,

Cost : 4 + 2x eqn 2

For a certain driving distance, the two companies charge the same total fare

Therefore, eqn 1 must be equal to eqn 2

26 + 1x = 4 + 2x

2x - 1x = 26 - 4

x = 22

Thus, for 22 kilometers, the two companies charge the same total fare

What is the total fare?

Substitute x = 22 in eqn 2

Cost: 4 + 2(22) = 4 + 44 = 48

Thus total fare is $ 48

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