Ms Newton's class took the same test as Mr. Euclid's students. Ms. Newton's class has 20 students, and the average(mean) test score was 90. The average of Mr. Euclids class was 80. If you combine both classes the average score on the test is 85. How many students does Mr. Euclid have in his Mathematics class?
To find the number of students in Mr. Euclid's class, we can use the concept of weighted averages.
Let's assume that Mr. Euclid's class has 'x' students.
The total number of students in both classes combined is 20 (Ms. Newton's class) + x (Mr. Euclid's class) = 20 + x.
The average score for Ms. Newton's class is given as 90, and the average score for Mr. Euclid's class is given as 80.
When we combine both classes, the average score is given as 85.
To find the number of students in Mr. Euclid's class, we can use the weighted average formula:
(20 * 90 + x * 80) / (20 + x) = 85.
Now, let's solve this equation to find the value of x, which represents the number of students in Mr. Euclid's class.
First, simplify the left side of the equation:
(1800 + 80x) / (20 + x) = 85.
Multiply both sides of the equation by (20 + x) to eliminate the denominator:
1800 + 80x = 85(20 + x).
Now, distribute the 85 to the terms in parentheses:
1800 + 80x = 1700 + 85x.
Next, subtract 80x and 1700 from both sides of the equation:
100 + 80x = 85x.
Subtract 85x from both sides of the equation:
100 = 5x.
Finally, divide both sides of the equation by 5 to isolate x:
20 = x.
Therefore, Mr. Euclid has 20 students in his Mathematics class.