How would you solve this problem. The mean of 10 numbers is 8. If an 11th number is now included, the mean becomes 9. What is the value of the 11th number? Make an algebraic solution.
mean = ∑x/n
9 = (10*8 + x)/11
Solve for x.
1.237
19
To solve this problem algebraically, we can start by setting up equations based on the given information.
Let's represent the sum of the 10 numbers by S and the value of the 11th number by x.
Since the mean of the 10 numbers is 8, we can write the equation:
S/10 = 8
If we include the 11th number, the mean becomes 9, giving us the equation:
(S + x)/11 = 9
To find the value of the 11th number (x), we can solve these two equations simultaneously.
1. Rearrange the first equation to solve for S:
S = 10 * 8
S = 80
2. Substituting the value of S into the second equation:
(80 + x)/11 = 9
3. Cross-multiply to get rid of the fraction:
80 + x = 99
4. Subtract 80 from both sides:
x = 99 - 80
x = 19
Therefore, the value of the 11th number is 19.