Answer: Let's assume the number of shoppers on the first day is "x."
Each day, the number of shoppers is 5 percent more than the previous day. So, on the second day, there will be 105% of the shoppers from the first day, which can be expressed as 1.05x. On the third day, there will be 105% of the shoppers from the second day, which is (1.05)(1.05x) = (1.05)^2x. This pattern continues for ten days.
The total number of shoppers over the first ten days can be represented as the sum of an arithmetic sequence with the first term "x" and the common ratio "1.05" for ten terms:
Sum = (n/2) * (first term + last term)
where n = 10 (number of days).
So, the sum of the first ten terms is:
1258 = (10/2) * (x + (1.05)^9 * x)
1258 = 5.5 * (1.05)^9 * x
Now, solve for x:
x = 1258 / (5.5 * (1.05)^9)
x ≈ 1258 / 6.329
x ≈ 198.64
Rounding to the nearest integer, the number of shoppers on the first day was 199.