Two Students Took An Examination In French, German, And Engl

Two Students Took An Examination In French German And Englishthe Inf

Two students took an examination in French, German, and English. The information below shows the marks for each subject and the weight to be applied to each subject. Subject, French, German, English. Student, Student, Weight 2 x 3. Calculate the value of X for which the two students have the same weighted mean mark and find the value of the mean.

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The problem involves determining the value of X such that two students have equal weighted mean marks across three subjects: French, German, and English. It also requires calculating this common mean. To approach this, we first interpret the data and understand the weighted mean formula, then set up the equations accordingly.

Suppose the marks of Student 1 are F1, G1, and E1 for French, German, and English respectively, and the marks of Student 2 are F2, G2, and E2. The weights for the subjects are 2, X, and 3 respectively, based on the given information. The weighted mean (WM) for each student is given by:

WM = (Subject marks × corresponding weights) / sum of weights

Let’s assume the specific marks for Student 1 and Student 2 are as follows based on typical exam scores, which could be provided in a detailed problem, but since they are not explicitly given, we consider general variables or numerical values for illustration.

Suppose Student 1’s marks are: F1, G1, E1; and Student 2’s marks are: F2, G2, E2. The weights are 2 for French, X for German, and 3 for English. The total weight sum is thus 2 + X + 3 = X + 5.

The weighted mean for Student 1:

WM1 = (2 × F1 + X × G1 + 3 × E1) / (X + 5)

The weighted mean for Student 2:

WM2 = (2 × F2 + X × G2 + 3 × E2) / (X + 5)

To find the value of X for which the two students have the same weighted mean, set WM1 = WM2:

(2F1 + XG1 + 3E1) / (X + 5) = (2F2 + XG2 + 3E2) / (X + 5)

Multiplying both sides by (X + 5) to clear denominators simplifies to:

2F1 + XG1 + 3E1 = 2F2 + XG2 + 3E2

Rearranged, this becomes:

XG1 - XG2 = 2F2 - 2F1 + 3E2 - 3E1

Factoring out X gives:

X(G1 - G2) = 2(F2 - F1) + 3(E2 - E1)

Finally, solving for X yields:

X = [2(F2 - F1) + 3(E2 - E1)] / (G1 - G2)

This is the general formula for X, demonstrating how X depends on the difference in marks for each subject between the two students.

To compute a numerical value, specific marks for each student in each subject are necessary. Once these are provided, simply plug in the values into the formula to obtain X.

Next, to find the value of the common weighted mean when the equality condition holds, substitute this X value back into either WM1 or WM2. This will give the mean mark both students share under the determined weight arrangement.

This approach emphasizes the importance of understanding weighted averages and algebraic manipulations in solving comparative performance problems in educational assessments.

References

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