Answer:
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
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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