Sunset rents an SUV at $21.95 plus $0.23 per mile. Sunrise rents the same vehicle for $24.95 plus $0.19 per mile. For what mileage is the cost the same?
2007-08-09 04:58:57 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
75 mph
2007-08-09 05:30:16 · answer #1 · answered by Anthony W 2 · 0⤊ 0⤋
Let x be the miles for which the rents are the same.
21.95 + 0.23x = 24.95 + 0.19x
0.23x - 0.19x = 24.95 - 21.95
0.04x = 3
x = 3/0.04 = 300/4 = 75
So, 75 miles is the answer. Since the difference per mile is just 4 cents, 75 miles will cost 3 dollars which is the difference in basic rent.
2007-08-09 05:07:04 · answer #2 · answered by Swamy 7 · 0⤊ 0⤋
If we define the total cost to be "x," then the total cost for any given mileage for the 2 cars is:
c1(x) = 21.95 + 0.23x
c2(x) = 24.95 + 0.19x
Since, we want the mileage when the cost is the same, let's the the two cost functions equal to each other ( c1(x) = c2(x) ) and solve for mileage "x":
21.95 + 0.23x = 24.95 + 0.19x
==> subtract 21.95 from both sides
0.23x = 3.00 + 0.19x
==> subtract 0.19x from both sides
0.04x = 3.00
==> divide by 0.04 on both sides
x = 3.00 / 0.04 = 75
So, your ANSWER is 75 miles.
By the way, if you want to know how much it will actually cost, just plug this mileage back into either function:
c1(75) = 21.95 + 0.23(75) = $39.20
2007-08-09 05:01:51 · answer #3 · answered by C-Wryte 4 · 0⤊ 0⤋
The problem can be defined by the following equation -
21.95 + 0.23x = 24.95 + 0.19x
where x is the number of miles
Solving for x -
0.23x - 0.19x = 24.95 - 21.95
0.04x = 3
x = 3/0.04
x = 75
The cost would be the same for a mileage of 75 miles
2007-08-09 05:04:34 · answer #4 · answered by MedievalLoser 2 · 0⤊ 0⤋
for d miles, sunset's cost 21.95+0.23d
and sunrise's cost 24.95+0.19d
21.95+0.23d=24.95+0.19d
0.04d=3
d=3/0.04=75 miles
2007-08-09 05:08:43 · answer #5 · answered by cidyah 7 · 0⤊ 0⤋
Let x = mileage.
Equation:
$21.95 + $0.23x = $24.95 + $0.19x
$0.23x - $0.19x = $24.95 - $21.95
$0.04x = $3.00
x = $3.00 / $0.04
x = 75
Answer: 75 miles
Proof (substitute x with 75):
$21.95 + $0.23x = $24.95 + $0.19x
$21.95 + $0.23(75) = $24.95 + $0.19(75)
$21.95 + $17.25 = $24.95 + $14.25
$39.20 =$39.20
2007-08-13 04:41:18 · answer #6 · answered by Jun Agruda 7 · 2⤊ 0⤋
21.95 + .23x = 24.95 + .19x, so .04x = 3, or x = 75.
same cost for 75 miles ($39.20)
2007-08-09 05:03:10 · answer #7 · answered by John V 6 · 0⤊ 0⤋
wow like that was so hard...75
2007-08-09 05:07:54 · answer #8 · answered by heidilocks 2 · 0⤊ 0⤋