## Monday, September 9, 2013

### Chicken, Rabbit Questions : Algebra Without Using Variables

The problems below are much easier so if you are preparing for the state, try the online timed test here.
Just write down random name to enter the test site is fine. At the end of the test, you'll see the answers for the ones you get wrong. Everyone is welcome to take the test. Thanks a lot and have fun problem solving.

#1: There are 20 horses and chickens at Old Macdonald's farm. Together there are 58 legs. How many horses and how many chickens?

Solutions I :
#1: Using algebra, you have
H + C = 20---equation 1 and
4H +2C = 58---equation 2

To get rid of one variable you can times equation 1 by 2 to get rid of Chicken or times 4 to get rid of horses.
Times 2 and you have 2 H + 2 C = 40 (every term needs to be multiplied by 2)---equation 3
4 H + 2C = 58---equation 2
Using equation 2 - equation 3 and yo get 2H = 18 so H = 9 and from there, solve for C = 11

Solution II:
Let there be C chickens and (20-C) horses. [Since the sum of the number of chickens and horses is 20. If one has C number, the other has (20 - C)

2C + 4 (20 - C) = 58;  2C + 80 - 4C = 58; -2C = -22; C = 11
and from there, you get H = 20 - 11 = 9

Solution III:
Without using algebra, you can make all the animals be chickens first. In that case, you'll have 20 x 2 = 40 legs.  Since you have 58 legs, you need to get rid of some chickens and bring in more horses.

You gain 2 legs by every transaction (-2 + 4 = 2).  (58 - 40) / 2 = 9 so 9 horses and 11 chickens.

Other similar questions to practice (answer key below):
#1: Rabbits and ducks -- 30 animals and  86 feet.
#2: There are 24 three-leg stools and four-leg tables. Together there are 86 legs.
#3: There are 43 bicycles and tricycles and together there are 100 wheels.
#4: There are 33 octopus (8 arms) and sea otters and together they have 188 arms/or for sea otters--legs. How many octopus and how many sea otters?
#5: There are 18 animals in the barnyard, some are cows and some are chickens. There are total 48 legs. How many chickens and how many cows?