Certainly! To find the third number given that the mean of three numbers is 40 and the first two numbers are 23 and 51, follow these steps:
1. Understand Mean Calculation:
- The mean (average) of numbers is the sum of the numbers divided by the number of values:
[tex]\[
\text{Mean} = \frac{\text{Sum of the numbers}}{\text{Number of values}}
\][/tex]
2. Set Up the Equation:
- We are given the mean (40) and the number of values (3). Let's denote the three numbers as [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex].
- Given two of the numbers, [tex]\( a = 23 \)[/tex] and [tex]\( b = 51 \)[/tex], the third number [tex]\( c \)[/tex] needs to be found.
3. Calculate the Total Sum:
- Multiply the mean by the number of values to get the total sum of the three numbers:
[tex]\[
\text{Sum of the numbers} = \text{Mean} \times \text{Number of values} = 40 \times 3 = 120
\][/tex]
4. Determine the Sum of the Known Numbers:
- Add the first two known numbers:
[tex]\[
\text{Sum of the first two numbers} = a + b = 23 + 51 = 74
\][/tex]
5. Find the Third Number:
- Subtract the sum of the first two numbers from the total sum to find the third number:
[tex]\[
c = \text{Total sum} - \text{Sum of the first two numbers} = 120 - 74 = 46
\][/tex]
Therefore, the third number is 46.
