Question

the average reading score of 17 - year - olds on certain tests is given by $y = 0.192x+244.26$ points, where $x$ is the number of years after 1950. assuming that this model was valid, write and solve an inequality that describes when the average 17 - year - old’s reading score on this test was between but not including 247 and 250. which of the following inequalities describes the situation correctly? \\(\bigcirc\\) a. $247>0.192x + 244.26>250$ \\(\bigcirc\\) b. $247\leq0.192x + 244.26\leq250$ \\(\bigcirc\\) c. $247\geq0.192x + 244.26\geq250$ \\(\bigcirc\\) d. $247<0.192x + 244.26<250$ between the years \\(\square\\) and \\(\square\\), the average 17 - year - old’s reading score was between but did not include 247 and 250.

Explanation:

Step1: Select correct inequality

The problem states the score $y$ is between but not including 247 and 250, so $247 < 0.192x + 244.26 < 250$. This matches option D.

Step2: Isolate the middle term

Subtract 244.26 from all parts:
$247 - 244.26 < 0.192x < 250 - 244.26$
$2.74 < 0.192x < 5.74$

Step3: Solve for x

Divide all parts by 0.192:
$\frac{2.74}{0.192} < x < \frac{5.74}{0.192}$
$14.27 < x < 29.89$

Step4: Convert to calendar years

Since $x$ is years after 1950, calculate:
$1950 + 14 = 1964$, $1950 + 30 = 1980$
We use whole years as $x$ represents full years after 1950.

Answer:

Correct inequality: D. $247 < 0.192x + 244.26 < 250$
Between the years 1964 and 1980, the average 17-year-old's reading score was between but did not include 247 and 250.