Question 142395: Car rental agency A will rent a car for $35 per day and an additional charge of $.24 per mile. Car rental agency B will only charge $.16 per mile but charges $41 per day. If adam wanted to rent a car for 3 days, how many miles would adam have to drive to make car rental agency b a better bargain?
Found 2 solutions by stanbon, jojo14344:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Car rental agency A will rent a car for $35 per day and an additional charge of $.24 per mile.
A(x) = 35d + 0.24m
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Car rental agency B will only charge $.16 per mile but charges $41 per day.
B(x) = 41d + 0.16 m
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If adam wanted to rent a car for 3 days, how many miles would adam have to drive to make car rental agency b a better bargain?
A(3,m) = 105 + 0.24m
B(3,m) = 123 + 0.16m
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INEQUALITY:
123+0.16m < 105 + 0.24m
18 < 0.08m
m > 225 minutes (B is a better buy if Adam drives more than 225 miles.
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Cheers,
Stan H.
Answer by jojo14344(1513) (Show Source):
You can put this solution on YOUR website! First, we'll make an equation for both car rental on how much they will charge. And we'll refer on these equations in making car rental B a better bargain.
For A = Rate ($/day) + 0.24* # of miles ------ eqn 1
For B = Rate ($/day) + 0.16* # of miles ------ eqn 2
We know the Rate but we don't know the # of miles he needs to travel, if we do trial and errror could take a awhile right?
So if we can exlude first the "rate of # of miles" in both eqn. and we'll see;
For A = $35/day * 3days= $105
For B = $41/day * 3days= $123
So you see in 3 days, B is +$18. Therefore, Adam needs to drive more in 3days to get the better deal right? How much more? And that's we'll find out,
We use the "rate of # of miles for both then", and plus $19 on A to get over the plus $18 of B, so B will be cheaper. To show,
Since # of miles unknown, we'll assign "x" to it,
Rate of A + $19 = Rate of B
$0.24* x(# of miles) +$19 = $0.16* x(# of miles)
$0.24x-$0.16x=-$19
$0.08x=-$19
x=-237.50 miles. There's no negative(-) miles, so we use 237.50 miles!
This is the total # of miles (minimum) Adam needs to travel so he can start his savings. To show that
For A, as per eqn 1 =($35*3days) + ($0.24*237.50mi)= $105+$57
A=$162
For B, as per eqn 2 =($41*3days) + ($0.41*237.50mi)=$123+$38
B=$161
There you go! Adam can start getting a dollar($1) cheaper if he drives at least 237.50miles in 3 days. The more miles he drives, the more savings he can get (if he compare it to Car Rental A)
Thank you,
Jojo
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