Every item in the Just a Dollar store is priced $1.00. When Jack opens the store, there is $175.00 in the cash register. When he counts the money in the cash register at the end of the day, the total is $1,003.40. If the sales tax rate is 9%, how many items were sold that day?

[end total - start total] / 1.09

x items were sold for $X.

x + 0.09x = 1003.40 - 175,
X = $760 and 760 item.

To find out how many items were sold, we need to calculate the total sales amount, including sales tax.

Step 1: Calculate the sales amount without tax:
The amount in the cash register at the start of the day is $175.00.
The amount in the cash register at the end of the day is $1,003.40.
Therefore, the total sales without tax is $1,003.40 - $175.00 = $828.40.

Step 2: Calculate the total sales amount with tax:
To calculate the sales amount with tax, we need to divide the total sales without tax by (100% + tax rate):
Tax rate = 9% = 9/100 = 0.09.
Total sales amount with tax = $828.40 / (1 + 0.09) = $828.40 / 1.09 = $760.

Step 3: Calculate the number of items sold:
Since each item is priced at $1.00, the number of items sold is equal to the total sales amount with tax.
So, the number of items sold that day is $760.

To find out how many items were sold that day, we need to calculate the total sales amount before taxes.

We know from the problem that the starting amount in the cash register was $175.00, and at the end of the day, it was $1,003.40. The difference between these two amounts gives us the total sales before taxes.

Total sales before taxes = $1,003.40 - $175.00 = $828.40

Since every item in the store is priced at $1.00, we can divide the total sales before taxes by the price of each item to find the number of items sold.

Number of items sold = Total sales before taxes / Price per item

Number of items sold = $828.40 / $1.00 = 828.4

However, keep in mind that we can't have a fraction of an item, so we need to round the number down to the nearest whole number since we can't sell a fraction of an item.

Therefore, the number of items sold that day is 828.