Question

Matthew's average mark in physics, chemistry and biology is x. If the average mark in history and geography was y , find his average mark for all the exams

Answer 1

To find Matthew's average mark for all the exams, we can follow these steps:

1. Let the total marks in physics, chemistry, and biology be represented as \( T_1 \). Since his average mark in these three subjects is \( x \), we can express \( T_1 \) as:
\[
T_1 = 3x
\]
(because there are three subjects).

2. Let the total marks in history and geography be represented as \( T_2 \). Since the average mark in these two subjects is \( y \), we can express \( T_2 \) as:
\[
T_2 = 2y
\]
(because there are two subjects).

3. The total marks for all the subjects (which includes physics, chemistry, biology, history, and geography) will then be:
\[
T_{\text{total}} = T_1 + T_2 = 3x + 2y
\]

4. The total number of subjects is \( 3 + 2 = 5 \).

5. Now, we can find the overall average mark by dividing the total marks by the total number of subjects:
\[
\text{Average mark} = \frac{T_{\text{total}}}{\text{Number of subjects}} = \frac{3x + 2y}{5}
\]

Thus, Matthew's average mark for all the exams is:
\[
\frac{3x + 2y}{5}
\]