Question 142395
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