Problema Solution
a student wants to buy one of two cars. one gets 32 mpg and costs 10000. the other cars gets 25 mpg and costs 8000. if gas is 4.00 \gal and he will travel 300mi/month, when will the total of each car be equal?
Answer provided by our tutors
Lets denote with 't' the time (in months) after the totals of each car will be equal.
After t time:
First car will spend 10000 + (t * 300) / 32 * 4 dollars
Second car will spend 8000 + (t * 300) / 25 * 4 dollars
Since the total money spent for the first car is equal to the total money spent for the second car we have the follwoing equation:
10000 + (t * 300) / 32 * 4 = 8000 + (t * 300) / 25 * 4
(t * 300) / 25 * 4 - (t * 300) / 32 * 4 = 10000 - 8000
48 * t - (75/2) * t = 2000
(48*2 - 75)/2 * t = 2000
(96 - 75) / 2 * t = 2000
21 / 2 * t = 2000
t = 2000 * 2 / 21
t = 4000/21 months
t = 190 months and (10 / 21 * 30) days
t = 190 months 14,3 days aproximately
t = 15 years 10 months (100/7) days ( = 15*12 + 10 + 10 / 21 = 4000 / 21 months)
After 15 years 10 months and 14,3 days aproximately the total of each car will be equal.