Word ProblemS

Question

In 1980 the average price of a home in Brainerd County was $94,000. By 1987 the average price of a home was $108,000. Which of the following is a linear model for the price of a home, P, in Brainerd County in terms of the year, t? Let t = 0 correspond to 1980.

 

[A] P = 108,000 - 2000t

[B] P = 14,000t + 94,000
[C] P = 2000t + 94,000

[D] P = 108,000 -14,000t

Answer 1

 

Let t = 0 correspond to 1980 and base price is $94,000.

When you have many options and have only 1 options to select, try to eliminate answers, we can identify options with 94,000 in it. We are left with option b and option c now

 

In 7 years, price increased from $94,000 to $108,000 i.e. $14,000

In a linear model, 14,000 is distributed linear in 7 years. therefore, in 1 year, price rise would be 14,000/7 = 2000. 

Therefore in t years, price rise would be 2000t

 

Hence, answer is

(C) 2000t + 94,000