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#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:
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.
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.
#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?
#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?
Answers:
#1: 13 rabbits and 17 ducks.
#2: 10 three-leg stools and 14 four-leg tables.
#3: 29 bicycles and 14 tricycles. #4: 14 octopus and 19 sea otters.
#5: 6 cows and 12 chickens.
