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?

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?

3.) 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?

I'm looking for work shown, too, please! :)

Answer 1

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:

Answer 2

Answer: i know im a tad late here.

# 1: 56= 8 people shakes hands. There are 8 hand shakers and each handshake with 7 other people. It means one person handshakes with 7 people.

# 2: 200 divided by 4= 50 so 30 pigs is 120 legs and 40 chickens which is 80 legs

# 3. im not good at graphs. i do believe the other person made one through.

hope you have a good day, love. and sorry for my answer being late.