How do I tell a markup problem from a discount problem?

By the direction word: "off," "discount," "sale," and "decrease" subtract from the original; "markup," "tax," "tip," and "increase" add to it. Circle that word before you compute anything.

How do I find the original price if I only know the sale price?

Express the sale price as a fraction of the original: after 25% off, it is 75% of the original, so divide the sale price by 0.75. Never subtract the percent of the sale price — the percent was applied to the original, not the sale price.

What is the fastest way to compute a percent of a number?

Convert to a decimal and multiply: 30\% of 80 is 0.3 \times 80 = 24. For mental math, find 10% first (move the decimal) and scale: 10% of 80 is 8, so 30% is 24.

What is the difference between percent change and percentage points?

Going from 20% to 25% is a change of 5 percentage points, but a 25% relative increase (\frac{5}{20}). News and statistics mix these up constantly — word problems usually want the relative percent change.

Can Photo Math Solver read the whole word problem, not just numbers?

Yes — screenshot the full sentence and it translates the words into an equation as an explicit first step, so you see how "\84 after a 40% markup" becomes 1.4p = 84 before any arithmetic happens.

You can start solving percentage problems for free by adding the Chrome extension — try it on your own homework before deciding if you need anything more.

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Photo Math Solver Solved

A restaurant bill is $80. How much is a 15% tip, and what is the total?

1Translate: the tip is $15\%$ of $80$ , so $0.15 \times 80 = 12$ .
2The tip is $12.
3The question also asks the total: $80 + 12 = 92$ dollars.

On this page01Definition 02Formulas 03Methods 04Examples 05Practice 06Mistakes 07FAQ

01Definition

What are percentage word problems?

Percentage word problems describe a part-whole relationship in a sentence: a discount off a price, a markup on a cost, a tip on a bill, a score improvement. The percent connects a part to its whole: $\text{part} = \frac{\text{percent}}{100} \times \text{whole}$ .

The arithmetic is rarely the hard part — the translation is. Every problem gives you two of the three quantities (part, percent, whole) and asks for the third, but hides which is which behind words like "off," "of," "markup," and "after."

The trickiest variant runs backwards: "the price after a 40% markup is $84 — what was the original?" Here $84 is not the whole but 140% of it, and recognizing that is the entire battle.

Where you'll actually use this

Shopping: stacking a 20% discount with a coupon, or checking whether "40% off" beats "buy one get one half off."
Money: tips, sales tax, interest on savings, and loan rates are all percent calculations.
School and work: grade improvements, population growth, and profit margins are percent-change problems.
News literacy: telling a 5-percentage-point change apart from a 5% relative change.

02Formulas

The formulas you need

Keep these on hand — every method below builds on them.

The percent equation

\text{part} = \frac{p}{100} \times \text{whole}

Two of the three are always given; solve for the third.

Increase / markup

\text{new} = \text{original} \times \left(1 + \tfrac{p}{100}\right)

A 40% markup multiplies by 1.40 in one move.

Decrease / discount

\text{new} = \text{original} \times \left(1 - \tfrac{p}{100}\right)

A 20% discount multiplies by 0.80.

Percent change

\%\,\text{change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100

Always divide by the OLD value, not the new one.

03Methods

How to solve percentage word problems

Pick the method that fits the problem in front of you.

When to use it: Straight "what is

p\%

of this amount" questions: tips, tax, a share of a total.

1Convert the percent to a decimal: $30\% = 0.30$ .
2Multiply by the whole: $0.30 \times 80 = 24$ .
3Read the question again — some problems want the part itself, others want the total including it (bill + tip).

04Worked examples

Percentage Word Problems, solved step by step

From easy to hard — pick a problem to see its full solution.

A restaurant bill is $80. How much is a 15% tip, and what is the total?

1Translate: the tip is $15\%$ of $80$ , so $0.15 \times 80 = 12$ .
2The tip is $12.
3The question also asks the total: $80 + 12 = 92$ dollars.

Try it on your own percentage word problems homework

Photo Math Solver reads the entire word problem from a screenshot — the sentence, not just the numbers — and shows the translation step first: which value is the whole, which is the percent, what the question actually asks. Then it solves, step by step. No fishing numbers out of a paragraph, and no guessing whether to add or subtract the change.

05Practice

Now you try

Work each one on paper first, then check your answer.

Problem 1

What is 25% off of an $88 pair of shoes?

Problem 2

A meal costs $40. What is the total with a 15% tip?

Problem 3

After a 25% discount, a game costs $45. What was the full price?

Problem 4

A price rose from $80 to $92. What was the percent increase?

Stuck on your percentage word problems homework? Screenshot it

Percentage word problems hide the actual numbers inside a long sentence, making them tedious to retype. Screenshot the problem with Photo Math Solver and it will pull out the relevant numbers, show the translation into an equation, and walk through the same part/whole/percent steps.

06Common mistakes

Where points get lost

Each of these shows up on real graded work — and each has a simple fix.

The mistake	Why it happens	The fix
Stopping at the percent amount instead of answering the question.	Computing "20% of $50 = $10" feels like the finish line, but the question asked for the sale price.	Re-read the final sentence of the problem after computing. If it asks for a price, your answer should be a price — apply the add or subtract step.
Adding when the problem says decrease, or subtracting on a markup.	The direction hides in a single word — "off," "discount," "markup," "grew" — and it is easy to skim past.	Circle the direction word before computing. Off/discount/decrease → subtract; markup/tax/tip/increase → add.
Solving reverse problems by taking the percent of the FINAL price.	Given "$84 after a 40% markup," subtracting 40% of 84 (giving $50.40) feels symmetric — but the 40% was applied to the original, not the final.	Write the forward equation first: $1.40 \times p = 84$ , then divide. The original is $\frac{84}{1.4} = 60$ , not $84 - 33.60$ .
Dividing by the new value when computing percent change.	Both numbers are on the page, and the larger or more recent one attracts the division.	Percent change always compares to where you started: $\frac{\text{new} - \text{old}}{\text{old}} \times 100$ . From 60 to 75 is $\frac{15}{60} = 25\%$ , not $\frac{15}{75} = 20\%$ .

Photo Math Solver shows every intermediate step, so slips like these are easy to catch before they cost you marks.

07FAQ