Answer :
The 7th number needed to achieve an average of 35.8 is option D, 32.72. (option d).
To find the 7th number required to achieve an average of 35.8, you can use the formula for calculating averages. The average of a set of numbers is found by dividing the sum of those numbers by the total count of numbers.
Let's denote the sum of the first six numbers as [tex]\( S \),[/tex] and the 7th number as [tex]\( x \)[/tex]. The average of these seven numbers is given by:
[tex]\[ \text{Average} = \frac{S + x}{7} = 35.8 \][/tex]
We want to solve for [tex]\( x \)[/tex], so we rearrange the equation:
[tex]\[ S + x = 7 \times 35.8 \]\[ S + x = 250.6 \][/tex]
Now, if we know the sum [tex]\( S \)[/tex] of the first six numbers and substitute it into the equation above, we can solve for [tex]\( x \)[/tex]:
[tex]\[ S + x = 250.6 \]\[ x = 250.6 - S \][/tex]
To find which number from the options (A, B, C, D, E, F) completes this equation, calculate the sum of the first six numbers and subtract it from 250.6.
Let's assume the sum of the first six numbers is:
[tex]\[ S = a + b + c + d + e + f \][/tex]
Substitute [tex]\( S \)[/tex] into the equation:
[tex]\[ x = 250.6 - (a + b + c + d + e + f) \][/tex]
Compute the value of [tex]\( x \)[/tex] for each option to identify which one results in the desired average of 35.8. The correct choice among the given options will be the one that, when added to the sum of the first six numbers, achieves the required average of 35.8. (option d).
