Final answer:
Sam and William will have the same amount of money on Day 17 after setting up and solving the equation based on their starting amounts of money and daily spending rates.
Step-by-step explanation:
To determine on what day Sam and William will have the same amount of money, we need to create an equation based on the information given. Sam has $92 and spends $5 every day while William has $41 and spends $2 every day. If we let x represent the number of days after which they will have the same amount of money, we can set up the following equations:
Sam's money after x days: $92 - $5xWilliam's money after x days: $41 - $2x
To find when they have the same amount, we equate the two:
$92 - $5x = $41 - $2x
Now we solve for x:
$92 - $41 = $5x - $2x
$51 = $3x
x = $51 / $3
x = 17
Therefore, Sam and William will have the same amount of money on Day 17, which is option A.