### All Algebra 1 Resources

## Example Questions

### Example Question #1 : How To Find The Amount Of Sales Tax

A new computer costs $600 plus 7% sales tax. How much is the cost of the computer with added tax?

**Possible Answers:**

**Correct answer:**

# How to calculate the amount of sales tax?

- Convert tax percentage into a decimal by moving the decimal point two spaces to the left.
- Multiple the pre-tax value by the newly calculated decimal value in order to find the cost of the sales tax.
- Add the sales tax value to the pre-tax value to calculate the total cost.

## Calculating sales tax at time of purchase:

In order to calculate the sales tax of an item, we need to first multiply the pre-tax cost of the item by the sales tax percentage after it has been converted into a decimal. Once the sales tax has been calculated it needs to be added to the pre-tax value in order to find the total cost of the item. Let's start by working with an example. If a magazine costs $2.35 and has a 6% sales tax, then what is the total cost of the item. First, we need to convert the sales tax percentage into a decimal by moving the point two spaces to the left.

Now, we need to multiply the pre-tax cost of this item by this value in order to calculate the sales tax cost.

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

## Calculating the sales tax percentage of a total:

If we are given the total cost of an item or group of items and the pre-tax cost of the good(s), then we can calculate the sales tax percentage of the total cost. First, we need to subtract the pre-tax value from the total cost of the purchase. Next, we need to create a ratio of the sales tax to the pre-tax cost off the items. Last, we need to create a proportion where the pre-tax cost is related to 100% and solve for the percentage of the sales tax. Let's start by working through an example. If a person pays $245.64 for groceries that cost $220.00 pre tax, then what is the sales tax percentage for the items.

First, subtract the pre-tax value from the total cost of the items to find the sales tax cost.

Next, create a ratio of the sales tax to the pre-tax cost of the items.

Last, create a proportion where the pre-tax value is proportional to 100% and solve for the percentage of sales tax.

Cross multiply and solve.

Isolate the sales tax percentage to the left side of the equation by dividing each side by the pre-tax value.

Round to two decimal places since our answer is in dollars and cents.

Last, we can check this answer by calculating the sales tax percentage of the total as seen previously.

First, we need to convert the sales tax percentage into a decimal by moving the point two spaces to the left.

Now, we need to multiply the pre-tax cost of this item by this value in order to calculate the sales tax cost.

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

Our answers check out; therefore they are correct. Now, let's use this information to solve the given problem.

## Solution:

First, calculate the amount of sales tax by multiply the percent tax times the total cost:

Next, add the amount of tax to the price of the computer:

### Example Question #1 : How To Find The Amount Of Sales Tax

A couple buys a house for a total price of $319,000. If the total price includes a 6.75% sales tax, how much does the house cost before tax?

**Possible Answers:**

**Correct answer:**

# How to calculate the amount of sales tax?

- Convert tax percentage into a decimal by moving the decimal point two spaces to the left.
- Multiple the pre-tax value by the newly calculated decimal value in order to find the cost of the sales tax.
- Add the sales tax value to the pre-tax value to calculate the total cost.

## Calculating sales tax at time of purchase:

In order to calculate the sales tax of an item, we need to first multiply the pre-tax cost of the item by the sales tax percentage after it has been converted into a decimal. Once the sales tax has been calculated it needs to be added to the pre-tax value in order to find the total cost of the item. Let's start by working with an example. If a magazine costs $2.35 and has a 6% sales tax, then what is the total cost of the item. First, we need to convert the sales tax percentage into a decimal by moving the point two spaces to the left.

Now, we need to multiply the pre-tax cost of this item by this value in order to calculate the sales tax cost.

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

## Calculating the sales tax percentage of a total:

If we are given the total cost of an item or group of items and the pre-tax cost of the good(s), then we can calculate the sales tax percentage of the total cost. First, we need to subtract the pre-tax value from the total cost of the purchase. Next, we need to create a ratio of the sales tax to the pre-tax cost off the items. Last, we need to create a proportion where the pre-tax cost is related to 100% and solve for the percentage of the sales tax. Let's start by working through an example. If a person pays $245.64 for groceries that cost $220.00 pre tax, then what is the sales tax percentage for the items.

First, subtract the pre-tax value from the total cost of the items to find the sales tax cost.

Next, create a ratio of the sales tax to the pre-tax cost of the items.

Last, create a proportion where the pre-tax value is proportional to 100% and solve for the percentage of sales tax.

Cross multiply and solve.

Isolate the sales tax percentage to the left side of the equation by dividing each side by the pre-tax value.

Round to two decimal places since our answer is in dollars and cents.

Last, we can check this answer by calculating the sales tax percentage of the total as seen previously.

First, we need to convert the sales tax percentage into a decimal by moving the point two spaces to the left.

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

Our answers check out; therefore they are correct. Now, let's use this information to solve the given problem.

## Solution:

We can convert 6.75% to a decimal by dividing by 100.

If is the price of the house, then the sales tax is . The price of the house and the sales tax add up to $319,000.

Combe terms on the left.

Finally, divide both sides by 1.0675.

### Example Question #2 : How To Find The Amount Of Sales Tax

How much should someone be charged in sales tax on a $32 purchase if the tax rate is 7%?

**Possible Answers:**

**Correct answer:**

# How to calculate the amount of sales tax?

- Convert tax percentage into a decimal by moving the decimal point two spaces to the left.
- Multiple the pre-tax value by the newly calculated decimal value in order to find the cost of the sales tax.
- Add the sales tax value to the pre-tax value to calculate the total cost.

## Calculating sales tax at time of purchase:

In order to calculate the sales tax of an item, we need to first multiply the pre-tax cost of the item by the sales tax percentage after it has been converted into a decimal. Once the sales tax has been calculated it needs to be added to the pre-tax value in order to find the total cost of the item. Let's start by working with an example. If a magazine costs $2.35 and has a 6% sales tax, then what is the total cost of the item. First, we need to convert the sales tax percentage into a decimal by moving the point two spaces to the left.

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

## Calculating the sales tax percentage of a total:

If we are given the total cost of an item or group of items and the pre-tax cost of the good(s), then we can calculate the sales tax percentage of the total cost. First, we need to subtract the pre-tax value from the total cost of the purchase. Next, we need to create a ratio of the sales tax to the pre-tax cost off the items. Last, we need to create a proportion where the pre-tax cost is related to 100% and solve for the percentage of the sales tax. Let's start by working through an example. If a person pays $245.64 for groceries that cost $220.00 pre tax, then what is the sales tax percentage for the items.

First, subtract the pre-tax value from the total cost of the items to find the sales tax cost.

Next, create a ratio of the sales tax to the pre-tax cost of the items.

Last, create a proportion where the pre-tax value is proportional to 100% and solve for the percentage of sales tax.

Cross multiply and solve.

Isolate the sales tax percentage to the left side of the equation by dividing each side by the pre-tax value.

Round to two decimal places since our answer is in dollars and cents.

Last, we can check this answer by calculating the sales tax percentage of the total as seen previously.

First, we need to convert the sales tax percentage into a decimal by moving the point two spaces to the left.

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

Our answers check out; therefore they are correct. Now, let's use this information to solve the given problem.

## Solution:

Do not overthink a problem like this. All that the question is asking is, "How much is 7% of $32." This can be rewritten as:

Therefore, the answer to the question is $2.24.

### Example Question #1 : How To Find The Amount Of Sales Tax

The sales tax where Mary lives is 7.5%. How much will Mary pay in total for a shirt that sells for $44?

**Possible Answers:**

**Correct answer:**

# How to calculate the amount of sales tax?

- Convert tax percentage into a decimal by moving the decimal point two spaces to the left.
- Add the sales tax value to the pre-tax value to calculate the total cost.

## Calculating sales tax at time of purchase:

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

## Calculating the sales tax percentage of a total:

First, subtract the pre-tax value from the total cost of the items to find the sales tax cost.

Next, create a ratio of the sales tax to the pre-tax cost of the items.

Cross multiply and solve.

Round to two decimal places since our answer is in dollars and cents.

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

## Solution:

There are two ways to do this. The easiest way is to realize that the total cost is 107.5% of the price of the shirt. This is like saying, "What is 107.5% of 44?"

This can be rewritten as an equation:

You can also calculate the taxes first by taking 7.5% of 44:

Add this to 44 to get a total cost of $47.30.

Either method will work, but the first is quicker.

### Example Question #3 : How To Find The Amount Of Sales Tax

If the sales tax on an order is 4% and the final cost after taxes is $76.96, what is the pre-tax cost of the order?

**Possible Answers:**

**Correct answer:**

# How to calculate the amount of sales tax?

- Convert tax percentage into a decimal by moving the decimal point two spaces to the left.
- Add the sales tax value to the pre-tax value to calculate the total cost.

## Calculating sales tax at time of purchase:

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

## Calculating the sales tax percentage of a total:

First, subtract the pre-tax value from the total cost of the items to find the sales tax cost.

Next, create a ratio of the sales tax to the pre-tax cost of the items.

Cross multiply and solve.

Round to two decimal places since our answer is in dollars and cents.

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

## Solution:

There are two ways that you could set up this problem. For the first way, you would ask yourself, "$76.96 is 104% of what original price?" This would be represented as:

Likewise, you could start by asking yourself, "A 4% increase of what price ends up at $76.96?" This would be translated as:

Note that this is the same as the equation above.

Solve the first equation by dividing both sides by 1.04. This gives you $74.

### Example Question #6 : How To Find The Amount Of Sales Tax

If the amount of sales tax on an order is 8% and its post-tax cost is $59.40, what is the amount of tax included in the post-tax cost?

**Possible Answers:**

**Correct answer:**

# How to calculate the amount of sales tax?

- Convert tax percentage into a decimal by moving the decimal point two spaces to the left.
- Add the sales tax value to the pre-tax value to calculate the total cost.

## Calculating sales tax at time of purchase:

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

## Calculating the sales tax percentage of a total:

First, subtract the pre-tax value from the total cost of the items to find the sales tax cost.

Next, create a ratio of the sales tax to the pre-tax cost of the items.

Cross multiply and solve.

Round to two decimal places since our answer is in dollars and cents.

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

## Solution:

The easiest way to solve this problem is by realizing that you can apply an 8% tax to an amount by multiplying that amount by 108% or 1.08. You could thus say to yourself, "$59.40 is 108% of what original amount?" This can be rewritten as the following equation:

Dividing both sides by 1.08, you get .

Now, be careful! The question asks NOT for the original price but for the tax amount, or .

### Example Question #7 : How To Find The Amount Of Sales Tax

Jerry paid $135.04 after tax for $125.62 worth of groceries. What is the sales tax rate, to the nearest tenth of a percent, where he bought the groceries?

**Possible Answers:**

%

%

%

%

%

**Correct answer:**

%

# How to calculate the amount of sales tax?

- Convert tax percentage into a decimal by moving the decimal point two spaces to the left.
- Add the sales tax value to the pre-tax value to calculate the total cost.

## Calculating sales tax at time of purchase:

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

## Calculating the sales tax percentage of a total:

First, subtract the pre-tax value from the total cost of the items to find the sales tax cost.

Next, create a ratio of the sales tax to the pre-tax cost of the items.

Cross multiply and solve.

Round to two decimal places since our answer is in dollars and cents.

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

## Solution:

The amount of sales tax Jerry paid was .

The sales tax is given as a percent of the original price of the groceries before tax, so we calculate $9.42 as a percent of $125.62 with this equation:

The sales tax rate is 7.5%.

### Example Question #2 : How To Find The Amount Of Sales Tax

The sales tax in Williamsburg is 11%. What would the tax be on a purchase of $69.60?

**Possible Answers:**

**Correct answer:**

# How to calculate the amount of sales tax?

- Convert tax percentage into a decimal by moving the decimal point two spaces to the left.
- Add the sales tax value to the pre-tax value to calculate the total cost.

## Calculating sales tax at time of purchase:

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

## Calculating the sales tax percentage of a total:

First, subtract the pre-tax value from the total cost of the items to find the sales tax cost.

Next, create a ratio of the sales tax to the pre-tax cost of the items.

Cross multiply and solve.

Round to two decimal places since our answer is in dollars and cents.

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

## Solution:

To find the tax, multiply the pre-tax total times .11 (the decimal form of 11%). The result is $7.656. Since we're dealing with money, round it to the hundredths place, which gives you an answer of $7.66.

### Example Question #9 : How To Find The Amount Of Sales Tax

The sales price of a bicycle is $415. If a customer paid a total of $434.50 for this bicycle, what was the sales tax percentage?

**Possible Answers:**

**Correct answer:**

# How to calculate the amount of sales tax?

- Convert tax percentage into a decimal by moving the decimal point two spaces to the left.
- Add the sales tax value to the pre-tax value to calculate the total cost.

## Calculating sales tax at time of purchase:

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

## Calculating the sales tax percentage of a total:

First, subtract the pre-tax value from the total cost of the items to find the sales tax cost.

Next, create a ratio of the sales tax to the pre-tax cost of the items.

Cross multiply and solve.

Round to two decimal places since our answer is in dollars and cents.

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

## Solution:

The difference between the total price ($434.50) and the sales price ($415) is the tax ($19.50). To find the sales tax as a percentage of the sales price, divide the sales tax by the sales price and then multiply by 100:

### Example Question #3 : How To Find The Amount Of Sales Tax

In Pennsylvania, vendors must impose a 6% sales tax on non-essential items. If a Blu-Ray player costs $95, and is a non-essential item, how much will the total price be including sales tax?

**Possible Answers:**

**Correct answer:**

# How to calculate the amount of sales tax?

- Convert tax percentage into a decimal by moving the decimal point two spaces to the left.
- Add the sales tax value to the pre-tax value to calculate the total cost.

## Calculating sales tax at time of purchase:

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

## Calculating the sales tax percentage of a total:

First, subtract the pre-tax value from the total cost of the items to find the sales tax cost.

Next, create a ratio of the sales tax to the pre-tax cost of the items.

Cross multiply and solve.

Round to two decimal places since our answer is in dollars and cents.

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

## Solution:

First, calculate the amount of sales tax by multiply the percent tax times the total cost:

Next, add the amount of tax to the price of the computer:

Calculate the amount of sales tax:

Add the amount of sales tax to the original price:

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