Question

1.) There are 8 people in a room.

Answer 1

Hello there!

Question #1

There are 8 people in a room.Each person shakes hands with each of the other people once and only once.How many handshakes take place?

So, by considering this question, we know that they're 8 people in the room. Ok, we understand this. So, if each person would be giving a hand shake only (once), this would show us that the question is stating (EACH). So, one key word when coming to multiply would be the word "each". So, practically, we would just multiply the number by the number it self.

$\boxed{8*8=\bf64-8=56}$ or 8 x 7 = 56 (either way) 

There were 56 hand shakes in this whole room, that's al lot.

Question #2

A student has some pigs and some chickens.He finds that together they have 70 heads and 200 legs.How many pigs and how many chickens does he have? 

This is quite an interesting question. So, let's consider this below!

Chickens have: 2 legs, and 1 head.

Pigs have: 4 legs, and 1 head.

But look! There is a key point here. The key point would be the they're 70 heads. This would mean that sense they're 70 heads altogether, we would then divide this by 2.

$\boxed{(70\div2=\bf35) \ or \ (15+15) = 30$

Now we have considered that they're 40 chickens, and 30 pigs.

Question #3 (last question).

 A well is 10 feet deep.A frog climbs up 5 feet during the day, but falls back 4 feet at night.Assuming that the frog starts at the bottom of the well,how many days does it take the frog to get to the top? 

Let's consider this! So, if the frog were to start from the bottom of the well, and the well is 10. . . . .

$\boxed{5-4=1 \ feet}$. And by this happening every day, this would show us that it would take this poor frog (3.6 days) to get back to the top of the well.

Your answer: 3.6 days.

Answer 2

1. 8 people, every person would shake hands with 7 other people
1st person shakes hands with 7 people
2nd person shakes hands with 6 people ( they already shook hands with the first person)
3rd person shakes 5 hands
4th shakes 4 hands
5th person shakes 3 hands
6th person shakes 2 hands
7th person shakes 1 other hand
 total = 7 +6 +5 +4 +3 +2 1 = 28 handshakes total




2. P = 70-C
4P + 2C = 200
4(70-C) +2C = 200
280 - 4c + 2c = 200
280 -2c = 200
-2c = -80
c = -80 / -2 = 40 chickens 
70-40 = 30 pigs

3. 6 days = see picture: