Word problem

Question

The price of a certain new car increases by the same amount each year. The first year it was $19400 and in the 12th year it was $33700. In which year will the car cost $37600?

Answer 1

Since this is a personal finance question I plugged this into excel. Below is a copy of the cost of the car for each year.

 

Year
$
 
1
$19,400.00
 
2
$20,700.00
 
3
$22,000.00
 
4
$23,300.00
 
5
$24,600.00
 
6
$25,900.00
 
7
$27,200.00
 
8
$28,500.00
 
9
$29,800.00
 
10
$31,100.00
 
11
$32,400.00
 
12
$33,700.00
 
13
$35,000.00
 
14
$36,300.00
 
15
$37,600.00
<=

 

 

Answer 2

The difference between the 1st and 12th years is 11 years. Lets call the unknown increase "x."

 

So, 19400 + 11x = 33700 => x = $1300

 

All you have to do is solve for the year "y" when the cost of the car is $37,600. The equation is:

 

19400 + y(1300) = 37600 => 1300y = 37600-19400 = 18,200  => y = 18200 / 1300 = 14 years

 

This is 14 years AFTER the first year, so it's the 15th year