Respuesta :
Answer:
The least value of n is, 9.
Step-by-step explanation:
Let n be the number of sheep in Integer.
Mary(M) owned the number of sheep is n i.e, M = n sheep
Sam(S) had exactly four times as many sheep as Mary , i.e, S = 4 n sheep
As per the given condition Mary buys 17 extra sheep
Now, Mary has total number of sheep, M = n +17 sheep
And Sam sells 8 of his sheep that means he has now,
[tex]S = 4n -8[/tex]
But, Sam still has more sheep than Mary i.e, [tex]4n-8 > n+17[/tex]
Solve an inequality: [tex]4n-8 > n+17[/tex]
Add 8 both sides we get;
[tex]4n-8+8>n+17+8[/tex]
Simplify:
[tex]4n>n+25[/tex]
Now, subtract n from both the side, we get;
[tex]4n -n>n+25-n[/tex]
Simplify:
[tex]3n>25[/tex] or [tex]n>\frac{25}{3}=8.33333333[/tex]
Since n is the number of sheep in integer,
then the least value of n is, 9.
Number of sheep Mary owned = n
Number of sheep Sam owned = 4n
Mary buys 17 extra sheep, so [tex]n+17[/tex]
Sam sells 8 of his sheep so [tex]4n-8[/tex]
Inequality becomes,
[tex]4n-8\geqn+17[/tex]
Solving the inequality we get,
[tex]n\geq \frac{25}{3}[/tex]
