I'm the cost in dollars of an n-mile trip with supreme taxi service is given by 1.5+1.75n. 1.5 plus 1.75 n the cost of an n-mile trip using town taxi service is given by 1.9+1.6n. 1.9 plus 1.6 n for rides between 1 and 10 miles, which service would you choose? explain.

Compare the costs on both taxi services for rides of 1-10 miles. Which company's prices are generally lower for that range?

Let x = 1 mile.

Supreme: $1.50+$1.75(1) = $3.25; Town: $1.90 + $1.60(1) = $3.50

Next, let x = 10 miles:

Supreme: $1.50+$1.75(10) = $19.00; Town: $1.90 + $1.60(10) = $17.90

Sometimes Supreme is the cheaper option; sometimes Town is. At what # of miles are the charges the same?

Set the charge functions = to each other and solve for x:

$1.50+$1.75x = $1.90 + $1.60x

Combining like terms, we get:

$0.15x = $0.40, so that x = 2 2/3 miles.

Supreme is the cheaper, for trips of 1 - 2 2/3 miles; Town is the cheaper, for trips of 2 2/3 miles - 10 miles.

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