Financial Math – ASVAB Math Review

1.Sales Tax & Tips

Additional charges added to the subtotal of a purchase.

Total = Original Price × (1 + Rate) or Amount = Original Price × Rate

Sales tax and tips are added to the original cost. Convert the percentage to a decimal before multiplying.

Example

A meal costs $20, and the sales tax is 8%. What is the total cost of the meal including tax?

Show solution

Step 1: Convert 8% to a decimal: $$\frac{8}{100} = 0.08$$

Step 2: Calculate tax amount: 20 × 0.08 = $1.60

Step 3: Add tax to original price: 20 + 1.60 = $21.60

Practice problems

Problem 1
A pair of shoes costs $50, and the local sales tax rate is 6%. What is the total amount paid at checkout?

Show solution

Answer: $53.00

Step 1: Convert 6% to a decimal: $$\frac{6}{100} = 0.06$$
Step 2: Calculate tax amount: 50 × 0.06 = $3.00
Step 3: Calculate total cost: 50 + 3.00 = $53.00
Problem 2
The bill for a dinner at a restaurant is $80. If you want to leave a 15% tip for the server, how much tip should you leave?

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Answer: $12

Step 1: Convert 15% to a decimal: $$\frac{15}{100} = 0.15$$
Step 2: Calculate tip amount: 80 × 0.15 = $12.00
Step 3: Identify the final answer as the tip amount requested
Problem 3
A new smartphone costs $600. If the sales tax is 7% and you purchase it online, what is the total cost including tax?

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Answer: $642.00

Step 1: Convert 7% to a decimal: $$\frac{7}{100} = 0.07$$
Step 2: Calculate tax amount: 600 × 0.07 = $42.00
Step 3: Calculate total cost: 600 + 42.00 = $642.00

Remember

Always convert percentages to decimals by dividing by 100 before performing calculations.

2.Discounts

A reduction made from the gross (original) amount.

Sale Price = Original Price × (1 - Discount Rate)

Discounts are subtracted from the original price. The sale price is the remaining percentage of the cost.

Example

A jacket originally costs $80 and is on sale for 25% off. What is the sale price?

Show solution

Step 1: Convert 25% to a decimal: $$\frac{25}{100} = 0.25$$

Step 2: Calculate discount amount: 80 × 0.25 = $20.00

Step 3: Subtract discount from original price: 80 - 20 = $60.00

Practice problems

Problem 4
A television originally priced at $400 is discounted by 15%. What is the sale price of the television?

Show solution

Answer: $340

Step 1: Convert 15% to a decimal: $$\frac{15}{100} = 0.15$$
Step 2: Calculate discount amount: 400 × 0.15 = $60.00
Step 3: Subtract discount from original price: 400 - 60 = $340.00
Problem 5
A video game normally costs $60. If it is featured on a weekly special for 40% off, how much money do you save?

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Answer: $24

Step 1: Convert 40% to a decimal: $$\frac{40}{100} = 0.40$$
Step 2: Calculate discount amount: 60 × 0.40 = $24.00
Step 3: Identify the final answer as the discount amount saved
Problem 6
A mattress set costs $1000. During a holiday sale, it is offered at a 30% discount. What is the final sale price?

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Answer: $700

Step 1: Convert 30% to a decimal: $$\frac{30}{100} = 0.30$$
Step 2: Calculate discount amount: 1000 × 0.30 = $300.00
Step 3: Subtract discount from original price: 1000 - 300 = $700.00

Remember

Always convert percentages to decimals by dividing by 100 before performing calculations.

3.Finding the Original Price

Calculating the starting price before tax or discount was applied.

Original Price = Sale Price / (1 - Discount Rate) hoặc Original Price = Total Price / (1 + Tax Rate)

To find the original price before a discount or tax, divide the final price by the remaining or total percentage.

Example

A concert ticket is on sale for $45 after a 10% discount. What was the original price of the ticket?

Show solution

Step 1: Convert 10% to a decimal: $$\frac{10}{100} = 0.10$$

Step 2: Calculate the remaining percentage rate: $$1 - 0.10 = 0.90$$

Step 3: Divide sale price by the rate: $$\frac{45}{0.90} = 50.00$$

Practice problems

Problem 7
After a 20% discount, the price of a bicycle is $160. What was the original price of the bicycle?

Show solution

Answer: $200

Step 1: Convert 20% to a decimal: $$\frac{20}{100} = 0.20$$
Step 2: Calculate the remaining percentage rate: $$1 - 0.20 = 0.80$$
Step 3: Divide sale price by the rate: $$\frac{160}{0.80} = 200.00$$
Problem 8
The total bill for a toolbox including an 8% sales tax is $54. What was the original price of the toolbox before tax?

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Answer: $50

Step 1: Convert 8% to a decimal: $$\frac{8}{100} = 0.08$$
Step 2: Calculate the total percentage rate: $$1 + 0.08 = 1.08$$
Step 3: Divide total price by the rate: $$\frac{54}{1.08} = 50.00$$
Problem 9
A furniture store sells a couch for $630 during a 30% off clearance event. What was the retail price before the markdown?

Show solution

Answer: $900

Step 1: Convert 30% to a decimal: $$\frac{30}{100} = 0.30$$
Step 2: Calculate the remaining percentage rate: $$1 - 0.30 = 0.70$$
Step 3: Divide sale price by the rate: $$\frac{630}{0.70} = 900.00$$

Remember

Always convert percentages to decimals by dividing by 100 before performing calculations.

4.Percent Change

Finding the percentage increase or decrease between two values.

Percent Change = (Amount of Change / Original Amount) × 100

Find the absolute difference between the new and old amounts, divide by the original amount, and convert to a percentage.

Example

A gym membership increased from $40 to $50 per month. What is the percent increase?

Show solution

Step 1: Find the change amount: $$50 - 40 = 10$$

Step 2: Divide change by original value: $$\frac{10}{40} = 0.25$$

Step 3: Multiply by 100 to get percentage: $$0.25 \times 100 = 25\%$$

Practice problems

Problem 10
An electronics retailer lowered the price of a headphone set from $80 to $60. What is the percent decrease in price?

Show solution

Answer: 25%

Step 1: Find the change amount: $$80 - 60 = 20$$
Step 2: Divide change by original value: $$\frac{20}{80} = 0.25$$
Step 3: Multiply by 100 to get percentage: $$0.25 \times 100 = 25\%$$
Problem 11
The enrollment at a local high school rose from 800 students to 880 students over one year. What is the percent increase?

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Answer: 10%

Step 1: Find the change amount: $$880 - 800 = 80$$
Step 2: Divide change by original value: $$\frac{80}{800} = 0.10$$
Step 3: Multiply by 100 to get percentage: $$0.10 \times 100 = 10\%$$
Problem 12
A stock price fell from $50 per share to $35 per share. What is the percent decrease of the stock value?

Show solution

Answer: 30%

Step 1: Find the change amount: $$50 - 35 = 15$$
Step 2: Divide change by original value: $$\frac{15}{50} = 0.30$$
Step 3: Multiply by 100 to get percentage: $$0.30 \times 100 = 30\%$$

Remember

Always convert percentages to decimals by dividing by 100 before performing calculations.