Question

4 systems of equations: word problem practice objective: use the desmos graphing calculator to solve these real - world scenarios. for the first five, the equations are provided. for the last five, you must write the equations before graphing. the car rental company a rents a car for $40 plus $0.10 per mile ($y = 0.10x + 40$). company b rents it for $25 plus $0.25 per mile ($y = 0.25x + 25$). at what mileage is the cost identical? equations: $y = 0.10x + 40$ and $y = 0.25x + 25$

Explanation:

Step1: Set the two equations equal

To find when the costs are identical, set \( y = 0.10x + 40 \) equal to \( y = 0.25x + 25 \). So we have the equation:
\( 0.10x + 40 = 0.25x + 25 \)

Step2: Subtract \( 0.10x \) from both sides

Subtracting \( 0.10x \) from each side gives:
\( 40 = 0.15x + 25 \)

Step3: Subtract 25 from both sides

Subtracting 25 from both sides:
\( 15 = 0.15x \)

Step4: Solve for \( x \)

Divide both sides by \( 0.15 \):
\( x=\frac{15}{0.15}= 100 \)

Answer:

The mileage at which the cost is identical is 100 miles.