Question

On our first quiz Juan scored 82. Use a compound inequality to show the possible score x he got on his second test, if the average is strictly between 74 and 80

Answer 1

We determine the minimum and maximum scores that Juan needs to get in order to be within the strict average range. We let x be his score.
 
minimum:
     74 = (82 + x) / 2
The value of x from the equation is equal to 66.

maximum:
    80 = (82 + x )/2
 The value of x from the equation is equal to 78. 

Hence, Juan's score should fall between 66 and 78, inclusive. 

Answer:    66 ≤ x ≤ 78

Answer 2

Answer:

$66\leq x\leq78$

Step-by-step explanation:

Juan scored in first quiz = 82

Let x be the marks he scored in second test .

We are given that the average is strictly between 74 and 80

Average = $\frac{\text{Sum of all numbers}}{\text{number of tests}}$

So, minimum:  

$74 =\frac{ (82 + x)}{2}$

$74 \times 2 =82 + x$

$148=82 + x$

$148-82 = x$

$66 = x$

So, maximum:

$80 =\frac{ (82 + x)}{2}$

$80 \times 2 =82 + x$

$160=82 + x$

$160-82 = x$

$78 = x$

So, Juan score on second test is $66\leq x\leq78$

Where 66 and 78 are inclusive.

Hence Juan's score should fall between 66 and 78, inclusive.

$66\leq x\leq78$