Help me solve a mileage reimbursement problem.?

Question

I'm horrible at math and I'm trying to solve a real problem. Let me explain. there are two mileage reimbursement programs. One pays a fixed sum (431 dollars) plus miles driven X 20.5 cents. the other pays 44.5 cents per mile with no fixed sum added. What is the number of miles I must drive to make the reimbursement equal? I'm trying to pick which one will be a better program for me, so I want to know how many miles I must drive to make the second program worth it.

thanks so much for your help. I was forgetting to move the decimal place over because it was cents not dollars per mile. again, thanks a lot.

Answer 1

See your other question (and my answer therein) --- if you drive less than 1796 miles, go with plan A.

The 44.5 cents per mile deal only works if you drive 1796 miles or greater.

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Answer 2

431 + .205x = cost of first method
.445x = cost of second methodThe cost will be the same for each method when:
431 +.205x = .445x
431= .24x
x = 431/.24 = 1,795.8333 miles

Let's say you drive 2000 miles.
Then method 1 costs 431+ 2000*,205= $841
Method 2 would cost .445*2000 = $890

Let's say you drive 1700 miles.
Then method 1 costs 431+ 1700*,205= $779.5
Method 2 would cost .445*1700 = $756

So you can see Method 2 is best for mileage less than 1795.833, but for mileage greater than 1795.833 Method 1 is better.

Answer 3

Pick X as number of miles.

431 + 20.5X = 44.5X

431 = .445X - .205X

431 = .24X

X = 431/.24

X = 1795.83333

1795.8333 miles they are equl so any millage above that the second program is better.

Answer 4

is the fixed sum per haul or for handling etc etc..............what is the fixed sum for........................