Every item in the Just a Dollar store is priced at $1.00. When Mary Jo opens the store, there is $128.50 in the cash register. When she counts the money in the cash register at the end of the day, the total is $1023.10. If the sales tax rate is 6.5%, how many items were sold that day?

Question

Every item in the Just a Dollar store is priced at $1.00. When Mary Jo opens the store, there is $128.50 in the cash register. When she counts the money in the cash register at the end of the day, the total is $1023.10. If the sales tax rate is 6.5%, how many items were sold that day?

Can someone please help me with this problem. I never know how to set these problems up.

Answer 1

n items

each costs 1+.065 = 1.065
so
1.065 n = 1023.10 - 128.50

Answer 2

1023.10 - 128.50 = 894.6

894.6 / 1.065 = 840

Answer 3

Thank You both!!

I have another question that is similar to this one..
An accountant earns $3180 per month after receiving a 8.5% raise. What was the accountant's monthly income before the raise? Round your answer to the nearest cent.
What i thought you did was 3180*8.5%=270.3
3180-270.30=2909.70, but it says its not correct. Any ideas on how to do this?

Answer 4

To solve this problem, we need to use a system of linear equations.

Let's start by defining some variables:
- Let x be the number of items sold that day.
- Let s be the sales tax rate, which is 6.5% or 0.065 in decimal form.

We know that every item in the Just a Dollar store is priced at $1.00, so the total revenue from selling the items would be x dollars.

Now let's set up the equations:

1. We know that the initial amount of money in the cash register was $128.50. Since every item costs $1.00, the initial amount of money can also be expressed as 1x:

Initial amount = 1x = $128.50

2. We also know that at the end of the day, the total amount of money in the cash register was $1023.10, which includes the sales tax. Since the sales tax rate is 6.5%, we can calculate the sales tax amount as 0.065x:

Total amount = 1x + 0.065x = $1023.10

We now have a system of two equations with two unknowns. We can solve this system to find the value of x, which represents the number of items sold that day.

To solve the system, we'll use the method of substitution or combination. Let's use substitution in this case.

From equation 1, we have:
1x = $128.50
x = $128.50

Substitute this value of x into equation 2:
1x + 0.065x = $1023.10
1(128.50) + 0.065(128.50) = $1023.10

Now, solve for x:
128.50 + 8.3525 = $1023.10
136.8525 = $1023.10

So, the number of items sold that day is approximately 136.

Therefore, approximately 136 items were sold that day at the Just a Dollar store.