Ruby is deciding between two truck rental companies. Company A charges an initial fee of $70 for the rental plus $2.50 per mile driven. Company B charges an initial fee of $90 for the rental plus $1.50 per mile driven. Let A(x)A(x) represent the amount Company A would charge if Ruby drives xx miles, and let B(x)B(x) represent the amount Company B would charge if Ruby drives xx miles. Write the equation for each function and determine which company would be cheaper if Ruby needs to drive 15 miles with the rented truck.

Company A charges an initial fee of $70 for the rental plus $2.50 per mile driven
Company B charges an initial fee of $90 for the rental plus $1.50 per mile driven
A(x) represents the amount company A would charge if Ruby drives x miles, and B(x) represents the amount company B would charge if Ruby drives x miles

Write the equation for each function and determine which company would be cheaper if Ruby needs to drive 15 miles with the rented truck

∵ Company A charges an initial fee of $70 for the rental

∵ It costs $2.5 per mile driven

∵ A(x) represents the amount would charge if Ruby drives x miles

∴ A(x) = 2.5 x + 70

∵ Company B charges an initial fee of $90 for the rental

∵ It costs $1.5 per mile driven

∵ B(x) represents the amount would charge if Ruby drives x miles

∴ B(x) = 1.5 x + 90

The equation of each function

A(x) = 2.5 x + 70

B(x) = 1.5 x + 90

∵ Ruby needs to drive 15 miles with the rented truck

∴ x = 15

- Substitute x by 15 in the two equation to find the cheaper one

∵ A(15) = 2.5(15) + 70

∴ A(15) = 107.5

The amount Company A would charge if Ruby drives 15 miles is $107.5

∵ B(15) = 1.5(15) + 90

∴ B(15) = 112.5

The amount Company B would charge if Ruby drives 15 miles is $112.5

∵ $107.5 is less than $112.5

∴ A(15) < B(15)

∴ The company A would be cheaper

Company A would be cheaper if Ruby needs to drive 15 miles

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