Question

Customer feedback rating for 2 regions is given as follows:
where,
y: CSAT rating
x: Average age of customer

The x-intercept of the equation formed representing the average of both the surveys is ____.

• A. $\frac{59}{4}$
• B. -$\frac{295}{8}$
• C. -$\frac{59}{4}$
• D. $\frac{295}{8}$

Answer 1

The correct option is D $\frac{295}{8}$

Given: Data collected from the suverys
Taking average of both the expressions:
Average (y)
= [$\frac{2}{5}$x + $\frac{17}{2}$ + (- $\frac{6}{5}$x) + 21] ÷ 2
= [($\frac{2}{5}$x - $\frac{6}{5}$x) + ($\frac{17}{2}$ + 21 ) ] ÷ 2
= [-$\frac{4}{5}$x + $\frac{59}{2}$ ] ÷ 2
$\Rightarrow$ y = -$\frac{2}{5}$x+ $\frac{59}{4}$

x-intercept of the equation is given by substuting y = 0 in the given expression,
$\Rightarrow$ 0 = (-$\frac{2}{5}$x + $\frac{59}{4}$)
$\Rightarrow \frac{2}{5}$x = $\frac{59}{4}$
$\Rightarrow$ x = $\frac{295}{8}$

$\therefore$ x-intercept is $\frac{295}{8}$.