Sondra has a lot of cats ( which have four legs) and parakeets (which have two legs), but now other pets. Among her pets, Sondra counts 57 heads and 176 legs How many cats does she have?
Since each pet has one head,
If there are c cats, then the rest (57-c) are 'keets
So, counting the legs,
4c + 2(57-c) = 176
c = cats
p = parakeets
Sondra counts 57 heads means:
c + p = 57
Cat have four legs, parakeets have two legs.
Sondra counts 176 legs means:
4 c + 2 p = 176
Now you must solve system of two equations:
c + p = 57
4 c + 2 p = 176
The solution is:
c = 31 , p = 26
She have 31 cats
I suspect cats and birds have one head apiece
c + p = 57
4 c + 2 p = 176
4 c + 2( 57 - c) = 176
4 c + 114 - 2 c = 176
2 c = 62
c = 31 cats
To determine the number of cats Sondra has, we can solve a system of equations based on the given information.
Let's use the variables:
C = number of cats
P = number of parakeets
Based on the number of heads, we know that C + P = 57.
Since cats have four legs and parakeets have two legs, the total number of legs can be represented as:
4C + 2P = 176.
We can now solve this system of equations to find the value of C.
Method 1: Substitution Method
1. Rearrange the equation C + P = 57 to P = 57 - C.
2. Substitute this expression for P in the second equation: 4C + 2(57 - C) = 176.
3. Simplify the equation: 4C + 114 - 2C = 176.
4. Combine like terms: 2C + 114 = 176.
5. Subtract 114 from both sides of the equation: 2C = 62.
6. Divide both sides by 2: C = 31.
So, Sondra has 31 cats.
Method 2: Elimination Method
1. Multiply the first equation (C + P = 57) by 2, which yields 2C + 2P = 114.
2. Subtract this equation from the second equation (4C + 2P = 176): (4C + 2P) - (2C + 2P) = 176 - 114.
3. Simplify the equation: 2C = 62.
4. Divide both sides by 2: C = 31.
So, Sondra has 31 cats.
Either method can be used to arrive at the same result.