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3 years ago

Mary owned n sheep and Sam had exactly 4 times as many sheep as Mary.

Mathematics

2 answers:

Veseljchak [2.6K]3 years ago

8 0

Answer:

The least value of n is, 9.

Step-by-step explanation:

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,

But, Sam still has more sheep than Mary i.e,

Solve an inequality:

Add 8 both sides we get;

Simplify:

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

Simplify:

Since n is the number of sheep in integer,

then the least value of n is, 9.

Nostrana [21]3 years ago

8 0

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$9\, w^{2} - 100 = (3\, w - 10) \, (3\, w + 10)$ .

Step-by-step explanation:

Fact:

$\begin{aligned} & (a - b)\, (a + b)\\ =\; & a^{2} + a\, b - a\, b - b^{2} \\ =\; & a^{2} - b^{2} \end{aligned}$ .

In other words, $(a^{2} - b^{2})$ , the difference of two squares in the form $a^{2}$ and $b^{2}$ , could be factorized into $(a - b)\, (a + b)$ .

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$9\, w^{2} - 100 = (3\, w)^{2} - (10)^{2}$ .

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$\begin{aligned}& 9\, w^{2} - 100 \\ =\; & (3\, w)^{2} - (10)^{2} \\ = \; & (3\, w - 10)\, (3\, w + 10)\end{aligned}$ .

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