Final answer:
Kara earned $17.25. Monica earned the most at $48.50, and Kara the least at $17.25, so the difference between the greatest and least amount earned is $31.25.
Step-by-step explanation:
The problem given is a word problem involving linear equations. Monica earned twice as much as Samuel, and Samuel earned $7 more than Kara. Given that Monica earned $48.50, we can find what Kara earned by setting up an equation. Let's let K represent the amount Kara earned. Since Monica earned twice as much as Samuel, and Samuel earned $7 more than Kara, we can express Samuel's earnings as K + $7. Therefore, according to the problem, Monica's earnings, $48.50, can be written as 2(K + $7).
We set up the equation and solve for K:
2(K + $7) = $48.50
K + $7 = $24.25
K = $24.25 - $7
K = $17.25
So, Kara earned $17.25.
To find the difference between the greatest amount earned and the least amount earned, we subtract Kara's earnings from Monica's earnings:
$48.50 - $17.25 = $31.25
Therefore, the difference between the greatest and the least amount earned walking dogs is $31.25.