Question

The marks scored by 4 student in mathematics test are as follows Esi=92,Seth=85,Mary=65,Esi=x. 1.Write down an expression for the mean of the marks. If the mean is less than 80, write a linear inequality for the information. 3. Find the possible marks Esi scored in the test.​

Answer 1

any value of x that satisfies the given conditions (i.e., makes the mean of the marks equal to the given value) is a possible score for Esi in the test. For example, if we want the mean to be 80, we can substitute 80 for Mean in the expression above and solve for x.

Explanation:

Expression for the mean of the marks:

The mean of the marks is the sum of all the marks divided by the number of students. So, for this problem, the expression for the mean is:

Mean = (92 + 85 + 65 + x) / 4

Linear inequality for the mean being less than 80:

We can find the mean of the marks using the expression above:

Mean = (92 + 85 + 65 + x) / 4

To write a linear inequality for the mean being less than 80, we can set up the inequality:

(92 + 85 + 65 + x) / 4 < 80

We can then solve for x:

92 + 85 + 65 + x < 320

x < 320 - 92 - 85 - 65

x < 78

Therefore, if Esi scored less than 78 in the test, the mean of the marks would be less than 80.

Possible marks Esi scored in the test:

We can use the expression for the mean of the marks to solve for Esi's score. We know that the mean of the marks is:

Mean = (92 + 85 + 65 + x) / 4

And we know that Esi's score is x. So, we can substitute x with Esi's score and solve for it:

(92 + 85 + 65 + Esi) / 4 = Mean

Multiplying both sides by 4:

92 + 85 + 65 + Esi = 4 x Mean

Simplifying:

242 + Esi = 4 x Mean

Substituting Mean with its value:

242 + Esi = 4 x ((92 + 85 + 65 + x) / 4)

Simplifying:

242 + Esi = 92 + 85 + 65 + x

242 + Esi = 242 + x

Subtracting 242 from both sides:

Esi = x