3.2 Percent Word Problems: Tax, Markup, Discount, Commission & Simple Interest

Why Percent Word Problems Matter on the GED

Official indicator Q.3.d — "solve two-step, arithmetic, real world problems involving percents" — is the last of the four Q.3 indicators inside Quantitative Problem Solving (45% of the test). GED Testing Service names six specific example categories for Q.3.d: simple interest, tax, markups and markdowns, gratuities and commissions, and percent increase and decrease. Notice the phrase "two-step": these are never single-operation problems. Every Q.3.d item on the real test requires you to compute one quantity (an interest amount, a tax amount, a discount amount) and then combine it with a starting value to reach a final answer — which is exactly the pattern used in every worked example below.

Percent problems also connect backward to Q.3.a–c (the same ratio-and-proportion thinking underlies "percent" — a percent is just a ratio to 100) and forward into real financial-literacy contexts the GED deliberately tests: shopping, paychecks, and simple savings accounts. Because six named contexts recur again and again, memorizing the formula for each one is one of the highest-value investments you can make before test day.

Core Terms and Rules

• A percent is a ratio to 100. To convert a percent to a decimal for calculation, divide by 100 (18% = 0.18); to convert a decimal to a percent, multiply by 100.
• The base is the original or starting amount a percent is calculated from. Identifying the base correctly is the single most important step in every percent word problem.
• Markup increases a price above cost; markdown (or discount) decreases a price below the original price.
• Gratuity (a tip) and commission are both percents of a total bill or sale amount, paid to a service provider or salesperson.
• Simple interest is interest calculated only on the original principal (not on previously earned interest). The GED formula sheet gives the formula as $I = Prt$, where $I$ = interest, $P$ = principal, $r$ = annual interest rate (as a decimal), and $t$ = time in years.
• Percent increase/decrease measures how much a quantity changed relative to its original value, not its new value.

Reference Table: Percent Formulas for Q.3.d

Worked Example 1: Sales Tax (Two-Step)

A television costs $420 before tax. The local sales tax rate is 8%. What is the total price including tax?

Step 1 — find the tax amount: $420 \times 0.08 = $33.60$. Step 2 — add it to the original price: $420 + 33.60 = $453.60$. The shortcut is to combine both steps into one multiplication: $420 \times 1.08 = $453.60$.

Worked Example 2: Markup Then Markdown — the Classic Trap

A store buys an item for $50 and marks it up 30% for the shelf price. Later, the item goes on a 30% clearance discount off that marked-up price. What is the final price?

Step 1 — markup: $50 \times 1.30 = $65.00$. Step 2 — discount off the new base of $65: $65 \times 0.70 = $45.50$. The final price is not $50 — a 30% increase followed by a 30% decrease does not cancel out, because the second percent is taken from a different (larger) base than the first. This exact trap — assuming equal-percent moves cancel — appears repeatedly across GED percent items.

Worked Example 3: Commission

A real estate agent earns a 5% commission on the sale of a $240,000 home. How much commission does the agent earn?

$240{,}000 \times 0.05 = $12{,}000$. A common wrong-answer trap misplaces the decimal point (giving $1,200 or $120,000) from mis-converting 5% to 0.5 or 5.0 instead of 0.05 — always double-check that the decimal form of a percent under 100% is less than 1.

Worked Example 4: Simple Interest (Formula Sheet)

Sam deposits $1,500 in a savings account earning 3% simple annual interest. How much total interest will the account earn after 4 years, and what is the final balance?

Using $I = Prt$: $I = 1{,}500 \times 0.03 \times 4 = $180$. Final balance: $P + I = 1{,}500 + 180 = $1{,}680$. If a problem instead gives time in months (say, 18 months), convert to years first: $18 \div 12 = 1.5$ years, before plugging into the formula — skipping that conversion is a frequent source of wrong answers.

Worked Example 5: Percent Increase

A town's population grew from 15,000 to 16,950 over five years. What is the percent increase?

$(16{,}950 - 15{,}000) \div 15{,}000 \times 100 = 1{,}950 \div 15{,}000 \times 100 = 13%$. Dividing by the new value (16,950) instead of the original (15,000) is the most common error on percent-change items — it produces a smaller, wrong percentage.

Common Traps

Practice Questions

Try these before checking the takeaways below.