Let \( r \) represent the number of reindeer and \( s \) represent the number of snowbirds. We can set up the following equations based on the information provided:
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The total number of heads (which is the total number of animals) is given by: \[ r + s = 42 \]
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The total number of legs is given by: \[ 4r + 2s = 134 \] (since each reindeer has 4 legs and each snowbird has 2 legs).
Now, we can solve this system of equations.
First, we can solve the first equation for \( s \): \[ s = 42 - r \]
Next, we substitute this expression for \( s \) into the second equation: \[ 4r + 2(42 - r) = 134 \] Distributing the 2 gives: \[ 4r + 84 - 2r = 134 \] Combining like terms: \[ 2r + 84 = 134 \] Now, subtract 84 from both sides: \[ 2r = 134 - 84 \] \[ 2r = 50 \] Dividing both sides by 2: \[ r = 25 \]
Now that we have \( r \), we can find \( s \): \[ s = 42 - r = 42 - 25 = 17 \]
Thus, Kris has 25 reindeer and 17 snowbirds.
Final answer:
- Reindeer: 25
- Snowbirds: 17