The equation of each function
A(x) = 2.5 x + 70
B(x) = 1.5 x + 90
Company A would be cheaper if Ruby needs to drive 15 miles
Step-by-step explanation:
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
- 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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