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

`66\leq x\leq78`

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 =( (82 + x))/(2)`

`74 * 2 =82 + x`

`148=82 + x`

`148-82 = x`

`66 = x`

So, maximum:

`80 =( (82 + x))/(2)`

`80 * 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`

Answer 2

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