Question 254890
For business purposes Mr. John Smith wants to determine the difference between the costs of owning, and renting an automobile. He can rent a car for $140 per month on an annual base. Under this plan his cost per mile for gas and oil is $ 0.05. If he were to purchase the car, his fixed annual expense would be $ 1000 and other costs would amount to $ 0.1 per mile. What is the least number of miles he would have to drive per year to make renting no more expensive than purchasing? Approach the questions using EXEL.

EXEL should be EXCEL

rent: $140/month * 12 months/year = 140*12 = $1680/year
       x=number of miles
       1680+0.05*x
purchase: 1000+0.1*x

set these equal to each other and solve for x
1680+0.05*x=1000+0.1*x
put x's on one side and constants on the other
680=0.1*x-0.05*x=0.05*x

680/0.05 = x
x=13600

{{{graph(600,500,0,20000,0,10000,1680+0.05*x,1000+0.1*x)}}}
miles	cost renting	cost purchasing
x	1680+0.05x	1000+0.1x
0	1680	        1000
1000	1730	        1100
2000	1780		1200
3000	1830		1300
4000	1880		1400
5000	1930		1500
6000	1980		1600
7000	2030		1700
8000	2080		1800
9000	2130		1900
10000	2180		2000
11000	2230		2100
12000	2280		2200
13000	2330		2300
13100	2335		2310
13200	2340		2320
13300	2345		2330
13400	2350		2340
13500	2355		2350
13600	2360		2360