Question

1. nick and liz have decided to move from the city to the suburbs. this means that they will have to make the essential purchase of a car in order to get to work. they researched used 2 - year - old cars of the same make, model, condition, and equipped with the same options. they found a website stating that the average price should be $18,500. these are the prices they were quoted: $15,500 $18,800 $16,900 $19,900 $18,000 $21,000 if they continued their search for one more price quote, what would that price have to be so that the mean of all seven of the car prices would be the same as the mean quoted on the website? $18,500 $19,000 $19,400 $19,900

Explanation:

Step1: Calculate sum of given 6 prices

$15500 + 18800+16900 + 19900+18000+21000=100100$

Step2: Let the seventh - price be $x$. Set up mean equation

The mean of 7 prices should be 18500. The formula for the mean $\bar{x}=\frac{\text{Sum of all values}}{\text{Number of values}}$. So, $\frac{100100 + x}{7}=18500$.

Step3: Solve the equation for $x$

Multiply both sides of the equation by 7: $100100 + x=18500\times7$.
$18500\times7 = 129500$. Then $x=129500 - 100100$.
$x = 19400$

Answer:

$19400$