Company A charges a $80 annual fee plus a $10/hr car share fee. Company B
charges $125 plus $5/hr. What is the minimum number of hours that a car
share needs to be used per year to make Company B a better deal?
O A. 9
OB. 6
O C. 11
OD. 10
Let's start by setting up an equation to compare the total cost of using each company for a certain number of hours in a year:
Total cost for Company A = $80 + $10/hr × number of hours used
Total cost for Company B = $125 + $5/hr × number of hours used
We want to find the minimum number of hours used where the total cost for Company B is less than or equal to the total cost for Company A:
$125 + $5/hr × number of hours used ≤ $80 + $10/hr × number of hours used
Simplifying this inequality, we get:
$45 ≤ $5/hr × number of hours used
Dividing both sides by $5/hr, we get:
9 ≤ number of hours used
So the minimum number of hours that a car share needs to be used per year to make Company B a better deal is 9 hours.
Therefore, the answer is A. 9.
To compare the two deals and determine which is better, we need to find the minimum number of hours of car share usage per year that makes Company B a better deal than Company A.
For Company A, the annual cost is $80 plus $10 per hour. Let's represent the total cost as C_A in terms of the number of hours:
C_A = $80 + ($10/hr) * h
For Company B, the cost is $125 plus $5 per hour. Let's represent the total cost as C_B in terms of the number of hours:
C_B = $125 + ($5/hr) * h
We want to find the value of h where C_B is less than C_A:
C_B < C_A
$125 + ($5/hr) * h < $80 + ($10/hr) * h
To simplify the equation, we'll isolate the h term by subtracting $80 and $125 from both sides:
($5/hr) * h - ($10/hr) * h < $80 - $125
Simplifying further:
-$5/hr * h < -$45
To remove the negative sign, we'll multiply both sides by -1:
$5/hr * h > $45
Next, divide both sides by $5/hr to find the value of h:
h > $45 / ($5/hr) = $45 * (hr/$5) = 9hr
Therefore, the minimum number of hours that a car share needs to be used per year to make Company B a better deal is 9 hours.
So, the answer is A. 9