Question 151689
First, we'll express the two rates as equations:
{{{R[1] = 72/d + 0.16/m}}} Rate 1 is $72 per day + $0.16 per mile.
{{{R[2] = 144/d + 0.08/m}}} Rate 2 is $144 per day + $0.08 per mile.
Since you are renting for one week (7 days) and letting x = the number of miles, we can refine the equations a bit:
{{{R[1] = 72(7)+0.16x}}}={{{504+0.16x}}}
{{{R[2] = 144(7)+0.08x}}}={{{1008+0.08x}}}
Now the question is, what value of x (number of miles) will make {{{R[2]<R[1]}}}, so we need to write the inequality:
{{{1008+0.08x < 504+0.16x}}} Now we solve this inequality for x. Subtract 0.08x from both sides.
{{{1008 < 504+0.08x}}} Now subtract 504 from both sides.
{{{504 < 0.08x}}} Finally, divide both sides by 0.08
{{{6300 < x}}} or {{{x > 6300}}}
So, you would need to drive more than 6300 miles to pay less with rate 2.
Let's check the answer by driving 6301 miles (6301 > 6300):
{{{R[1] = 504+0.16(6301)}}}
{{{R[1] = 504+1008.16}}}
{{{R[1] = 1512.16}}}
Rate 1 would be $1512.16 for one week's rental driven 6301 miles.
{{{R[2] = 1008+0.08(6301)}}}
{{{R[2] = 1008+504.08}}}
{{{R[2] = 1512.08}}}
Rate 2 would be $1512.08 for one week's rental driven 6301 miles.
So you can see that if you were to drive more than 6300 miles for the week, rate 2 would cost you less than rate 1.