adobe rent a car company charges a $50 rental free ,$20 for gas and $0.20 per mile driven for the same car vamos card charges $55 for rental and gas and $0.30 per mile . A find the number of miles for which the companies charge will be the same then find that charge show your work

We want to find the number of miles for which both companies charge the same amount.

We will see that the number of miles such that the costs are equal is 150 miles, and both companies charge $100 for that number of miles.

Adobe charges $50 for rental, $20 for gas and $0.20 per mile drive, so if you drive for x miles, the cost is:

A(x) = $50 + $20 + $0.20*x = $70 + $0.20*x

While we know that Vamos card charges $55 for rental and gas (together) and $0.30 per mile, so if you drive for x miles the cost is:

V(x) = $55 + $0.30*x

We want to find the value of x such that the cost equations are equal, so we must solve:

A(x) = V(x)

$70 + $0.20*x = $55 + $0.30*x

$70 - $55 = $0.30*x - $0.20*x

$15 = $0.10*x

$15/$0.10 = x = 150

So for 150 miles, both companies charge the same amount.

The cost is:

V(150) = A(150) = $70 + $0.20*150 = $100

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x = 150 miles

Cost = $100

Step-by-step explanation:

Company A = 50 + 20 + 0.20x

= 70 + 0.20x

Company B = 55 + 0.30x

Where,

x =number of miles

find the number of miles for which the companies charge will be the same

Equate the charges of both companies

70 + 0.20x = 55 + 0.30x

70 - 55 = 0.30x - 0.20x

15 = 0.10x

Divide both sides by 0.10

x = 15 / 0.10

= 150

x = 150 miles

The number of miles for which the companies charge will be the same is 150 miles

Substitute 150 miles into any of the companies charges to find the charge

Company B = 55 + 0.30x

= 55 + 0.30(150)

= 55 + 45

= $100