Question
At a university, the arithmetic mean of the final grades of a group of 5 students in a discipline was 72. Three of these students obtained the following grades: 65, 70 and 80. The two other students got the same grade. Determine the grade of the remaining two students:
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Answer to a math question At a university, the arithmetic mean of the final grades of a group of 5 students in a discipline was 72. Three of these students obtained the following grades: 65, 70 and 80. The two other students got the same grade. Determine the grade of the remaining two students:
Esmeralda
4.794 Answers
1. The arithmetic mean equation is:
\frac{65 + 70 + 80 + 2x}{5} = 72
2. Calculate the sum of the first three grades:
65 + 70 + 80 = 215
3. Substitute into the mean equation:
\frac{215 + 2x}{5} = 72
4. Multiply both sides by 5 to eliminate the denominator:
215 + 2x = 360
5. Solve for \( x \):
2x = 360 - 215
2x = 145
6. Divide both sides by 2 to find \( x \):
x = 72.5
The grade of the remaining two students is 72.5 each.
2. Calculate the sum of the first three grades:
3. Substitute into the mean equation:
4. Multiply both sides by 5 to eliminate the denominator:
5. Solve for \( x \):
6. Divide both sides by 2 to find \( x \):
The grade of the remaining two students is 72.5 each.
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