Question

Multiple chickens and rabbits are in a cage. There are 20 more chickens than rabbits and together, there are 256 legs in all. How many rabbits are there? Please explain

Answer 1

c = −108 and r = 118

Explanation:

Since we know that chickens have 2 legs and rabbits have 4 legs, we can set up a system of equations to solve the problem.

Let c be the number of chickens and r be the number of rabbits.

for legs, we can write the equation out in word form as:

(number of legs per chicken)(number of chickens) + (number of legs per rabbit)(number of rabbits) = (total number of rabbits)

In algebraic form, this equation would look like this:

2 c + 4 r = 256

20+r +r = 256

Now we can use elimination (or substitution) to solve for c and r:

The equation can be reduced by dividing both sides by 2:

c + 2 r = 128

Solve for r.

20+r +r = 256

2r = 236

2r/2 = 236/2

r = 118

Substitute and solve for c.

c + 2(118) = 128

c + 236 = 128

c = -108