In a Yoga Class there were 12 members. Two members left the class and 4 new members joined. If the average age decreased by 4 years and the total age decreased by 2. What is the new average age of the class? (in years)
Question
In a Yoga Class there were 12 members. Two members left the class and 4 new members joined. If the average age decreased by 4 years and the total age decreased by 2. What is the new average age of the class? (in years)
Solution
Sure, let's solve this step by step:
Step 1: Initially, there were 12 members in the class. Let's assume the initial average age was 'x' years. So, the total age of the class was 12x years.
Step 2: Two members left and 4 new members joined. So, the total number of members in the class became 12 - 2 + 4 = 14.
Step 3: The average age decreased by 4 years, so the new average age is x - 4 years.
Step 4: The total age of the class decreased by 2 years, so the new total age is 12x - 2 years.
Step 5: The total age is also equal to the average age times the number of members. So, we can set up the equation: (x - 4) * 14 = 12x - 2.
Step 6: Solve this equation to find the value of 'x'.
Multiplying through the brackets gives: 14x - 56 = 12x - 2.
Rearranging gives: 14x - 12x = 56 + 2.
Solving gives: 2x = 58.
So, x = 58 / 2 = 29 years.
So, the initial average age was 29 years.
Step 7: The new average age is x - 4 = 29 - 4 = 25 years.
So, the new average age of the class is 25 years.
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