Question

A student scored 84 and 87 on her first two quizzes.Write and solve a compound inequality to find the possible values for a third quiz score that would give her an average between 85 and 90 inclusive.

Answer 1

Mean of data = sum of values ÷ number of data

We have three values; 84, 87, and $x$

Sum of values = $84+87+x$ = $171+x$

We want the value of $x$ to give mean between 85 and 90 inclusive

$85 \leq \frac{171+x}{3} \leq 90$
$85*3 \leq 171+x \leq 90*3$
$255 \leq 171+x \leq 270$
$255-171 \leq x \leq 270-171$
$84 \leq x \leq 99$

Hence, the value of $x$ is between 84 and 99 inclusive

Answer 2

Answer:

The score in third quiz must be lie between 84 to 99 inclusive.

Step-by-step explanation:

Let the marks in third quiz be x.

The student scored 84 and 87 on her first two quizzes.

The formula for mean is

$Mean=\frac{\text{Sum of observations}}{\text{No. of observations}}$

$Mean=\frac{84+87+x}{3}$

$Mean=\frac{171+x}{3}$

The average between 85 and 90 inclusive.

$85\leq\frac{171+x}{3}\leq90$

$85\times 3\leq171+x\leq 90\times 3$

$255\leq171+x\leq 270$

$255-171\leq x\leq 270-171$

$84\leq x\leq 99$

Since the value of x lies between between 84 to 99 inclusive, therefore the score in third quiz must be lie between 84 to 99 inclusive.