Given that the mean score for four females and six males is 24.
Let 'b' represent a boy's score and 'g' represent a girl's score.
\(4g + 6b = 10\times24 = 240 ......(1)\)
The condition is \(b≤g≤2b\).
We need to find the possible values of \( 2g + 6b = 2g + 240 - 4g = 240 - 2g\).
From (1), if b = g, then 10g = 240, which implies g = 24.
The expression 240 - 2g ranges from \(240 - 2\times24\) when b = g, to \(240 - 2\times \frac{240}{7}\) when \(b = \frac{g}{2}\).
\(b = \frac{g}{2}\) implies \(4g + 6(\frac{g}{2}) = 240\),
\(⇒\) \(4g + 3g = 240\)
\(⇒\) \(7g = 240\)
\(⇒\) \(g =\frac{ 240}{7} \)
Thus, the range of values for 240 - 2g is from 192 to approximately 171.42.
\(⇒\) The integer values in this range are from 172 to 192, totaling 21 values.
The average of three distinct real numbers is 28. If the smallest number is increased by 7 and the largest number is reduced by 10, the order of the numbers remains unchanged, and the new arithmetic mean becomes 2 more than the middle number, while the difference between the largest and the smallest numbers becomes 64.Then, the largest number in the original set of three numbers is