Math Snap

STEP 1

Assumptions1. The average price of a new car in2014 is $37,600. The price of new cars increases by approximately $1250 per year3. We want to find out when the average price of a new car will be $43,850

STEP 2

First, we need to find out how much the price of a new car needs to increase to reach $43,850. We can do this by subtracting the initial price from the target price.
$$Price\, increase = Target\, price - Initial\, price$$

STEP 3

Now, plug in the given values for the target price and initial price to calculate the price increase.
Price\, increase = \($\)43,850 - \($\)37,600

STEP 4

Calculate the price increase.
Price\, increase = \($\)43,850 - \($\)37,600 = \($\)6,250

STEP 5

Now that we have the price increase, we can find out how many years it will take for the price of a new car to increase by this amount. We can do this by dividing the price increase by the annual increase in price.
$$Years = Price\, increase / Annual\, increase$$

STEP 6

Plug in the values for the price increase and the annual increase to calculate the number of years.
Years = \($\)6,250 / \($\)1,250

STEP 7

Calculate the number of years.
Years = \($\)6,250 / \($\)1,250 =5So, it will take5 years after2014 for the average price of a new car to reach $43,850.

STEP 8

To find out in which year this will occur, we can add the number of years to the initial year.
$$Year = Initial\, year + Years$$

STEP 9

Plug in the values for the initial year and the number of years to calculate the year.
$$Year =2014 +5$$

Calculate the year.
$$Year =2014 +5 =2019$$So, the average price of a new car will reach $43,850 in the year2019.