Final answer:
After 29 days, Sam will have saved $108.75. This is calculated by finding the sum of an arithmetic series, which represents the total number of quarters she saved, and then converting that sum into dollars.
Step-by-step explanation:
The question is asking for the total amount of money Sam will have saved after 29 days if she saves an increasing number of quarters each day, starting with 1 quarter on the first day and adding one more quarter each subsequent day. This is a problem related to arithmetic series in mathematics where we need to find the sum of a sequence of numbers.
To solve this, we can use the formula for the sum of the first n natural numbers:
S = n(n + 1) / 2,
where S is the sum and n is the total number of terms.
In Sam's case, n is 29 days. Plugging this into the formula:
S = 29(29 + 1) / 2 = 29(30) / 2 = 435 quarters in total.
Since four quarters make a dollar, we divide the total number of quarters by 4 to find out how many dollars Sam saved:
$108.75 (435 ÷ 4 = 108.75).
Therefore, after 29 days, Sam will have saved $108.75.