Question

Mary owned n sheep and Sam had exactly 4 times as many sheep as Mary. Mary buys 17 extra sheep and Sam sells 8 of his sheep. Sam still has more sheep than Mary. Form an inequality, in terms of n. Solve the inequality to find the least value of n. You must show all your working.

Answer 1

The least value of n is, 9.

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,

`S = 4n -8`

But, Sam still has more sheep than Mary i.e,
`4n-8 > n+17`

Solve an inequality:
`4n-8 > n+17`

Add 8 both sides we get;

`4n-8+8>n+17+8`

Simplify:

`4n>n+25`

Now, subtract n from both the side, we get;

`4n -n>n+25-n`

Simplify:

`3n>25` or
`n>(25)/(3)=8.33333333`

Since n is the number of sheep in integer,

then the least value of n is, 9.