Question

There are 6 more chickens than rabbits. The number of legs is 50 more than the number of heads. How many chickens and how many rabbits are there?

Answer 1

Apply algebra in word problems is a good way to check if you can understand the concept of algebra and applying it to solve real world problem.

Define x:

Let the number of rabbits be x.

The number of chicken = x + 6

Find the total number of heads:

*Each animal has 1 head.

Total number of heads = x + x + 6

Total number of heads = 2x + 6

Find the total number of legs:

chicken has 2 legs.

Rabbits has 4 legs.

Total number of chicken legs = x(x + 6)

Total number of chicken legs = 2x + 12

Total number of rabbit legs = 4x

Total number of legs = 2x + 12 + 4x

Total number of legs = 6x + 12

Given that there are 50 more legs than the number of head:

6x + 12 = 2x + 6 + 50

6x + 12 = 2x + 56

4x = 44

x = 11

Find the number of rabbits and chickens:

Rabbits = x

Rabbits = 11

Chickens = x + 6

Chickens = 11 + 6

Chickens = 17

Answer: There are 11 rabbits and 17 chickens.

Check:

Total number of heads:

Total animals = 11 + 17

Total animals = 28

Total number of legs:

chicken legs = 17 x 2

chicken legs= 34

Rabbit legs = 11 x 4

Rabbit legs = 44

Total legs = 34 + 44

Total legs = 78

Difference:

Difference between legs and head = 78 - 28

Difference between legs and head = 50

Answer 2

Answer:

★Number of chickens and rabbits are 11 and 17 respectively ★

Step-by-step explanation:

Given:

• There are 6 more chickens than rabbits
• Also, The number of legs is 50 more than the number of heads.

To Find:

• Number of chickens and rabbits

Solution: Let number of Rabbits be x

∴ Number of Chickens will be x + 6

† Rabbits and Chickens have 1 head †

∴

→ Total number of Heads = ( Number of Rabbit's head + Number of Chicken's Head )

$\small\implies{\sf }$ (x)1 + (x + 6)1

$\small\implies{\sf }$ x + x + 6 = 2x + 6 Heads

→ Total number of Legs = ( Number of Rabbit's legs + Number of Chicken's legs )

★ Rabbits have 4 and Chickens have 2 legs ★

$\small\implies{\sf }$ (x)4 + (x + 6)2

$\small\implies{\sf }$ 4x + 2x + 12

$\small\implies{\sf }$ 6x + 12

According to the question, Equation will be :

$\small\implies{\sf }$ 2x + 6 + 50 = 6x + 12

$\small\implies{\sf }$ 2x + 56 = 6x + 12

$\small\implies{\sf }$ 56 – 12 = 6x – 2x

$\small\implies{\sf }$ 44 = 4x

$\small\implies{\sf }$ x = 11

Hence, The number of Rabbits = x = 11

and number of Chickens = x + 6 = 11 + 6 = 17