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R51 • Lesson 81 of 105

Percent Applications

Tax, tip, discount, and markup calculations in real-world contexts

Reserve & Extensions • K-12

Prerequisites: M17

Key Concepts

  • percent
  • tax
  • tip
  • discount
  • markup
  • applications

Percent Applications

Percentages show up everywhere in daily life -- sale prices, restaurant tips, tax bills, pay raises, and loan interest. Mastering percent calculations is one of the most practically useful math skills you can develop.

Core Percent Formula

Part = Percent × Whole

This formula can be rearranged to find any of the three values:

Find the...FormulaExample
PartPercent × Whole20% of 80 = 0.20 × 80 = 16
PercentPart ÷ Whole16 out of 80 = 16 ÷ 80 = 0.20 = 20%
WholePart ÷ Percent16 is 20% of what? 16 ÷ 0.20 = 80

Tax, Tip, and Discount

Worked Example 1: Sales Tax

A jacket costs $65.00. Sales tax is 8%. What is the total cost?

  1. Calculate tax: 0.08 × $65.00 = $5.20
  2. Add to price: $65.00 + $5.20 = $70.20

Shortcut: Multiply by 1.08 directly. $65.00 × 1.08 = $70.20

Worked Example 2: Discount Then Tax

A $120 pair of shoes is 25% off. Sales tax is 6%. What do you pay?

  1. Discount amount: 0.25 × $120 = $30
  2. Sale price: $120 - $30 = $90
  3. Tax on sale price: 0.06 × $90 = $5.40
  4. Total: $90 + $5.40 = $95.40

Tip: The Multiplier Shortcut

A 15% tip means you pay 100% + 15% = 115% of the bill. Multiply by 1.15. A 30% discount means you pay 100% - 30% = 70%. Multiply by 0.70. This one-step method is faster and reduces errors.

Percent Increase and Decrease

Percent Change = (New - Original) ÷ Original × 100%

Worked Example 3: Percent Increase

A town's population grew from 8,000 to 9,200. What was the percent increase?

  1. Change: 9,200 - 8,000 = 1,200
  2. Percent change: 1,200 ÷ 8,000 = 0.15 = 15%
  3. The population increased by 15%.

Finding the Whole from a Percent

Worked Example 4: Working Backwards

After a 20% discount, a TV costs $360. What was the original price?

  1. After a 20% discount, you pay 80% of the original.
  2. Set up: 0.80 × Original = $360
  3. Solve: Original = $360 ÷ 0.80 = $450

Common Mistake: Percent Change Uses the ORIGINAL

Always divide by the original value, not the new value. If a price goes from $50 to $60, the increase is $10 ÷ $50 = 20%, not $10 ÷ $60.

Practice Problems

1. A meal costs $42.00. You want to leave a 20% tip. How much is the total including tip?

Show Solution

Tip: 0.20 × $42 = $8.40. Total: $42.00 + $8.40 = $50.40. Or: $42 × 1.20 = $50.40.

2. A $250 bike is on sale for 30% off. Tax is 7%. What is the final price?

Show Solution

Sale price: $250 × 0.70 = $175. Tax: $175 × 0.07 = $12.25. Final: $175 + $12.25 = $187.25.

3. A stock went from $80 to $68. What is the percent decrease?

Show Solution

Change: $80 - $68 = $12. Percent decrease: $12 ÷ $80 = 0.15 = 15%.

4. 45 is 60% of what number?

Show Solution

Whole = Part ÷ Percent = 45 ÷ 0.60 = 75.

5. A store marks up items by 40% from wholesale cost. If the retail price is $63, what was the wholesale cost?

Show Solution

Retail = 1.40 × Wholesale. Wholesale = $63 ÷ 1.40 = $45.

Lesson Summary

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