Sondra has a lot of cats (which have four legs) and parakeets (which have two legs) but no other pets. Among her pets, Sondra counts 57 heads and 176 legs. How many cats does she have?
thanks this really helped my son
To solve this problem, we can set up a system of equations based on the given information. Let's denote the number of cats as 'c' and the number of parakeets as 'p'.
Since cats have four legs and parakeets have two legs, we can write an equation for the total number of legs:
4c + 2p = 176
Next, since Sondra has a total of 57 heads (cats + parakeets), we can write an equation for the total number of heads:
c + p = 57
Now we have a system of two equations:
4c + 2p = 176
c + p = 57
We can solve this system of equations to find the values of 'c' and 'p'.
To eliminate 'p' from the first equation, we can multiply the second equation by 2 and subtract it from the first equation:
(4c + 2p) - 2(c + p) = 176 - 2(57)
4c + 2p - 2c - 2p = 176 - 114
2c = 62
Divide both sides of the equation by 2:
2c/2 = 62/2
c = 31
So, Sondra has 31 cats.
number of cats -- c
number of parakeets -- 57-c , there were 57 heads and I assumed each animal had only one head.
4c + 2(57-c) = 176
4c + 114 - 2c = 176
etc