Question

problem of the week
problem c
math test math 1
dilip has had six tests in his math class so far. he knows the average (mean) of some of his marks.

• the average of his first and second test marks is 77%.
• the average of his third and fourth test marks is 75%.
• the average of his fifth and sixth test marks is 82%.

determine the average of all six test marks for dilip.

Explanation:

Step1: Find the sum of the first two tests

Let the first test mark be \(x_1\) and the second be \(x_2\). The average formula is \(\text{Average}=\frac{\text{Sum of values}}{\text{Number of values}}\). Given \(\frac{x_1 + x_2}{2}=77\), then \(x_1 + x_2=77\times2 = 154\).

Step2: Find the sum of the third and fourth tests

Let the third test mark be \(x_3\) and the fourth be \(x_4\). Since \(\frac{x_3 + x_4}{2}=75\), then \(x_3 + x_4=75\times2=150\).

Step3: Find the sum of the fifth and sixth tests

Let the fifth test mark be \(x_5\) and the sixth be \(x_6\). Given \(\frac{x_5 + x_6}{2}=82\), then \(x_5 + x_6=82\times2 = 164\).

Step4: Find the sum of all six tests

The sum of all six tests \(S=x_1 + x_2+x_3 + x_4+x_5 + x_6=(x_1 + x_2)+(x_3 + x_4)+(x_5 + x_6)=154 + 150+164=468\).

Step5: Calculate the average of all six tests

The average of the six - test marks \(\text{Average}=\frac{S}{6}\). Substituting \(S = 468\) into the formula, we get \(\frac{468}{6}=78\).

Answer:

\(78\%\)