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 ?

Answer 1

Let's denote the number of cats Sondra has as \( c \) and the number of parakeets as \( p \).

From the problem, we can derive the following two equations based on the information provided:

1. The total number of heads (which is the total number of pets): \[ c + p = 57 \]

2. The total number of legs (four legs for cats and two legs for parakeets): \[ 4c + 2p = 176 \]

Now, we can solve these equations step-by-step.

First, let's solve the first equation for \( p \): \[ p = 57 - c \]

Next, we substitute this expression for \( p \) into the second equation: \[ 4c + 2(57 - c) = 176 \]

Expanding this gives: \[ 4c + 114 - 2c = 176 \]

Now, combine like terms: \[ 2c + 114 = 176 \]

Subtract 114 from both sides: \[ 2c = 176 - 114 \] \[ 2c = 62 \]

Now divide by 2: \[ c = 31 \]

So, Sondra has 31 cats.

To find the number of parakeets, substitute \( c \) back into the equation for \( p \): \[ p = 57 - 31 = 26 \]

Thus, Sondra has 31 cats and 26 parakeets.

To verify:

• Number of heads: \( 31 + 26 = 57 \) (correct)
• Number of legs: \( 4 \times 31 + 2 \times 26 = 124 + 52 = 176 \) (correct)

The calculations hold true, confirming that Sondra has 31 cats.