Could you help me with this math question.
The mean of 4 numbers is 5 and the mean of 3 different numbers is 12. What is the mean of the 7 numbers combined? Produce an algebraic solution.
Of course! To find the mean of the 7 numbers combined, we need to determine the sum of all the numbers and then divide that sum by 7.
We are given two pieces of information: the mean of 4 numbers is 5, and the mean of 3 different numbers is 12. Let's represent these numbers algebraically.
Let the sum of the 4 numbers be S1, and the sum of the 3 different numbers be S2.
Since the mean of 4 numbers is 5, we can write the equation: S1/4 = 5.
To find the sum S1, we multiply both sides of the equation by 4: S1 = 4 * 5 = 20.
Similarly, since the mean of 3 different numbers is 12, we can write the equation: S2/3 = 12.
To find the sum S2, we multiply both sides of the equation by 3: S2 = 3 * 12 = 36.
Now, to find the mean of the 7 numbers combined, we need to find the sum of all the numbers (S1 + S2) and divide it by 7.
The sum of the 7 numbers is S1 + S2 = 20 + 36 = 56.
Finally, we divide the sum of the 7 numbers by 7 to find the mean: 56/7 = 8.
Therefore, the mean of the 7 numbers combined is 8.