### All ACT Math Resources

## Example Questions

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

Jim buys a pair of shoes for , including tax. If the shoes were priced at , what percentage tax rate was he charged?

**Possible Answers:**

%

**Correct answer:**

%

Step 1: Find the amount of tax tax paid

Jim paid including tax for shoes that were pre-tax. Therefore:

Jim paid in tax.

Step 2: Figure out the tax rate (What percentage of is ?)

Set up a proportion and solve for :

Therefore, Jim paid an tax on the shoes he purchased.

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

A new boat cost . If the sales tax rate is , what was the original price of this boat before sales tax?

**Possible Answers:**

**Correct answer:**

The easiest way to do this is to write out the equation as though you were solving from the original price to find the final price. You would know that:

or

Solving for , you get:

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

If a given locality charges sales tax, what is the total price for purchasing an item that costs before tax? Round to the nearest cent.

**Possible Answers:**

**Correct answer:**

If a given locality charges sales tax, what is the total price for purchasing an item that costs before tax?

First, convert to . Then, multiply this by to get dollars. Add this to the original price to get . This rounds to .

Another way to do this is to multiply to get the same amount.

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

Sarah is buying a shirt that she likes. The shirt costs but there is an sales tax. How much does Sarah pay for the shirt in total, after sales tax is added? (Round to the nearest cent.)

**Possible Answers:**

**Correct answer:**

To find how much total is payed for an item after sales tax, conver the sales tax to a decimal and add it to 1, then multiply that total to the price of the item.

### Example Question #1 : How To Find Simple Interest

Ben and Sam are starting a furniture design business. In order to build their shop, they borrow $150,000 from their neighborhood bank. The interest rate on the loan is 6%. How much interest do they have to pay?

**Possible Answers:**

$12,000

$3000

$9000

$1500

$6000

**Correct answer:**

$9000

Simple interest = Amount borrowed x Interest rate =

150,000 x 6% = 150,000 x .06 = $9000

### Example Question #1 : How To Find Simple Interest

Amy recently opened a new credit card. In her first month, expenditures totaled $500 and she was not charged any interest. Amy paid $80 from her first month's bill. The second month, Amy spent another $60 on her credit card. This time, she was charged 5% interest on her total unpaid balance. How much interest was Amy charged?

**Possible Answers:**

$4.80

$32.00

$24.00

$12.00

$48.00

**Correct answer:**

$24.00

This requires us to keep track of Amy's expenses. After her first month, the unpaid balance was 500 - 80 = $420.

However, after the second month, her unpaid balance went up to $480.

5% of 480 can be obtained by multiplying

480 x .05 = 24

### Example Question #1 : How To Find Simple Interest

Ella loaned Frances $10,000 to start a business. They agreed that the loan would be paid back in five years, with a simple interest rate of 9%. When the loan is paid back in full, what will be the total amount that Ella collects?

**Possible Answers:**

**Correct answer:**

The simple interest formula is given by I = PRt where I = interest, P = principal, R = rate, and t = time.

Here, I = 10,000 * 0.09 * 5 = $4,500.

The total repayment amount is the interest plus the principal, so $4,500 + $10,000 = $14,500 total repayment.

### Example Question #1 : How To Find Simple Interest

An account accrues of simple interest during a fifteen year period. If this is accrued yearly at a rate of , what was the initial balance of the account at the beginning of this period? Round to the nearest dollar.

**Possible Answers:**

**Correct answer:**

Simple interest has the formula of:

, where is the starting balance, is the interest rate, and is the number of accrual periods.

For our data, this is simply:

Simplifying, we get:

Divide both sides by to get:

### Example Question #1 : How To Find Simple Interest

An account accrues simple interest on an initial balance of dollars at a rate of per year. After years, how much interest has accrued to the account?

**Possible Answers:**

**Correct answer:**

Simple interest has the formula of:

, where is the starting balance, is the interest rate, and is the number of accrual periods.

For our data, this is simply:

### Example Question #1 : How To Find Simple Interest

The equation can be used to calculate simple interest, where is the total interest, is the principal amount, is the rate of interest expressed as a decimal and is the amount of times interest is added.

A man pays in annual interest on a loan of . If the loan repayment term was years, what was the interest rate?

**Possible Answers:**

**Correct answer:**

Plugging our variables into the above equation gives us

Thus, our interest rate is .

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