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

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 Link

wifilethbridge wifilethbridge · Answer 2 · 2019-05-01T07:02:21+02:00

Answer:

[tex]66\leq x\leq78[/tex]

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 = [tex]\frac{\text{Sum of all numbers}}{\text{number of tests}}[/tex]

So, minimum:

[tex]74 =\frac{ (82 + x)}{2}[/tex]

[tex]74 \times 2 =82 + x[/tex]

[tex]148=82 + x[/tex]

[tex]148-82 = x[/tex]

[tex]66 = x[/tex]

So, maximum:

[tex]80 =\frac{ (82 + x)}{2}[/tex]

[tex]80 \times 2 =82 + x[/tex]

[tex]160=82 + x[/tex]

[tex]160-82 = x[/tex]

[tex]78 = x[/tex]

So, Juan score on second test is [tex]66\leq x\leq78[/tex]

Where 66 and 78 are inclusive.

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

[tex]66\leq x\leq78[/tex]