Grade 7 · Ratios & Proportional Reasoning · MAT-07-RP-007
Solve Markup, Markdown, Tax, and Tip Problems
Represent and solve solve markup, markdown, tax, and tip problems problems using precise mathematical notation, models, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve solve markup, markdown, tax, and tip problems problems using precise mathematical notation, models, and reasoning.
- Explain why a method for solve markup, markdown, tax, and tip problems works, interpret the result in context, and verify it independently.
Prerequisite check
Make sure the foundation is ready.
The new lesson depends on this prerequisite as active knowledge.
Learn
Build the idea from meaning, not memorization.
Mathematical meaning
Solve Markup, Markdown, Tax, and Tip Problems is about multiplicative comparison. Equivalent representations preserve the same scale relationship, not merely the same difference.
Represent the relationship
The Math Box uses percent model to expose the structure. Change one input, predict the result, then connect the visual change to an equation, table, graph, number line, or geometric model.
Calculate, interpret, and verify
Verify with an inverse operation, equivalent representation, estimate, or second method so both the calculation and reasoning are auditable.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Percent Lab
Percent means “per 100.” Change the percent and the whole to see the part update.
- Model one example of solve markup, markdown, tax, and tip problems in the Math Box.
- Change one input, predict the effect, and test the prediction.
- State the relationship or invariant that explains what stayed mathematically consistent.
Worked examples
Twenty different ways to see the concept work.
A 40 amount has a 5% percent increase. Find the change and resulting amount.
change = 5/100 × 40 = 2; result = 42An increase, tax, or tip adds the percent change to the original amount.
A 45 amount has a 10% markdown. Find the change and resulting amount.
change = 10/100 × 45 = 4.5; result = 40.5A markdown reduces the original amount, so subtract the percent change.
A 50 amount has a 15% sales tax. Find the change and resulting amount.
change = 15/100 × 50 = 7.5; result = 57.5An increase, tax, or tip adds the percent change to the original amount.
A 55 amount has a 20% tip. Find the change and resulting amount.
change = 20/100 × 55 = 11; result = 66An increase, tax, or tip adds the percent change to the original amount.
A 60 amount has a 25% percent increase. Find the change and resulting amount.
change = 25/100 × 60 = 15; result = 75An increase, tax, or tip adds the percent change to the original amount.
A 65 amount has a 30% markdown. Find the change and resulting amount.
change = 30/100 × 65 = 19.5; result = 45.5A markdown reduces the original amount, so subtract the percent change.
A 70 amount has a 5% sales tax. Find the change and resulting amount.
change = 5/100 × 70 = 3.5; result = 73.5An increase, tax, or tip adds the percent change to the original amount.
A 75 amount has a 10% tip. Find the change and resulting amount.
change = 10/100 × 75 = 7.5; result = 82.5An increase, tax, or tip adds the percent change to the original amount.
A 80 amount has a 15% percent increase. Find the change and resulting amount.
change = 15/100 × 80 = 12; result = 92An increase, tax, or tip adds the percent change to the original amount.
A 85 amount has a 20% markdown. Find the change and resulting amount.
change = 20/100 × 85 = 17; result = 68A markdown reduces the original amount, so subtract the percent change.
A 90 amount has a 25% sales tax. Find the change and resulting amount.
change = 25/100 × 90 = 22.5; result = 112.5An increase, tax, or tip adds the percent change to the original amount.
A 95 amount has a 30% tip. Find the change and resulting amount.
change = 30/100 × 95 = 28.5; result = 123.5An increase, tax, or tip adds the percent change to the original amount.
A 100 amount has a 5% percent increase. Find the change and resulting amount.
change = 5/100 × 100 = 5; result = 105An increase, tax, or tip adds the percent change to the original amount.
A 105 amount has a 10% markdown. Find the change and resulting amount.
change = 10/100 × 105 = 10.5; result = 94.5A markdown reduces the original amount, so subtract the percent change.
A 110 amount has a 15% sales tax. Find the change and resulting amount.
change = 15/100 × 110 = 16.5; result = 126.5An increase, tax, or tip adds the percent change to the original amount.
A 115 amount has a 20% tip. Find the change and resulting amount.
change = 20/100 × 115 = 23; result = 138An increase, tax, or tip adds the percent change to the original amount.
A 120 amount has a 25% percent increase. Find the change and resulting amount.
change = 25/100 × 120 = 30; result = 150An increase, tax, or tip adds the percent change to the original amount.
A 125 amount has a 30% markdown. Find the change and resulting amount.
change = 30/100 × 125 = 37.5; result = 87.5A markdown reduces the original amount, so subtract the percent change.
A 130 amount has a 5% sales tax. Find the change and resulting amount.
change = 5/100 × 130 = 6.5; result = 136.5An increase, tax, or tip adds the percent change to the original amount.
A 135 amount has a 10% tip. Find the change and resulting amount.
change = 10/100 × 135 = 13.5; result = 148.5An increase, tax, or tip adds the percent change to the original amount.
Practice
Guided practice with hints
01A 140 amount has a 15% percent increase. Find the change and resulting amount.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: change = 15/100 × 140 = 21; result = 161
02A 145 amount has a 20% markdown. Find the change and resulting amount.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: change = 20/100 × 145 = 29; result = 116
03A 150 amount has a 25% sales tax. Find the change and resulting amount.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: change = 25/100 × 150 = 37.5; result = 187.5
04A 155 amount has a 30% tip. Find the change and resulting amount.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: change = 30/100 × 155 = 46.5; result = 201.5
05A 160 amount has a 5% percent increase. Find the change and resulting amount.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: change = 5/100 × 160 = 8; result = 168
06A 165 amount has a 10% markdown. Find the change and resulting amount.
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: change = 10/100 × 165 = 16.5; result = 148.5
Practice
Independent practice
01A 170 amount has a 15% sales tax. Find the change and resulting amount.
Answer: change = 15/100 × 170 = 25.5; result = 195.5
02A 175 amount has a 20% tip. Find the change and resulting amount.
Answer: change = 20/100 × 175 = 35; result = 210
03A 180 amount has a 25% percent increase. Find the change and resulting amount.
Answer: change = 25/100 × 180 = 45; result = 225
04A 185 amount has a 30% markdown. Find the change and resulting amount.
Answer: change = 30/100 × 185 = 55.5; result = 129.5
05A 190 amount has a 5% sales tax. Find the change and resulting amount.
Answer: change = 5/100 × 190 = 9.5; result = 199.5
06A 195 amount has a 10% tip. Find the change and resulting amount.
Answer: change = 10/100 × 195 = 19.5; result = 214.5
07A 200 amount has a 15% percent increase. Find the change and resulting amount.
Answer: change = 15/100 × 200 = 30; result = 230
08A 205 amount has a 20% markdown. Find the change and resulting amount.
Answer: change = 20/100 × 205 = 41; result = 164
Common mistakes
Learn to catch the error, not just the answer.
Check for a common scale factor or constant unit rate.
Convert both to a common unit rate first.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Compare prices, speeds, recipes, maps, taxes, discounts, tips, and rates using common units.
- Scale designs and predict related quantities while preserving multiplicative relationships.
Challenge problems
A 210 amount has a 25% sales tax. Find the change and resulting amount.
change = 25/100 × 210 = 52.5; result = 262.5
A 215 amount has a 30% tip. Find the change and resulting amount.
change = 30/100 × 215 = 64.5; result = 279.5
A 220 amount has a 5% percent increase. Find the change and resulting amount.
change = 5/100 × 220 = 11; result = 231
A 225 amount has a 10% markdown. Find the change and resulting amount.
change = 10/100 × 225 = 22.5; result = 202.5
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 7 Reasoning Sprint
Solve solve markup, markdown, tax, and tip problems problems accurately and justify each result with a valid check.
Practice
Mastery check
01A 230 amount has a 15% sales tax. Find the change and resulting amount.
Answer: change = 15/100 × 230 = 34.5; result = 264.5
02A 235 amount has a 20% tip. Find the change and resulting amount.
Answer: change = 20/100 × 235 = 47; result = 282
03A 240 amount has a 25% percent increase. Find the change and resulting amount.
Answer: change = 25/100 × 240 = 60; result = 300
04A 245 amount has a 30% markdown. Find the change and resulting amount.
Answer: change = 30/100 × 245 = 73.5; result = 171.5
05A 250 amount has a 5% sales tax. Find the change and resulting amount.
Answer: change = 5/100 × 250 = 12.5; result = 262.5
06A 255 amount has a 10% tip. Find the change and resulting amount.
Answer: change = 10/100 × 255 = 25.5; result = 280.5
07A 260 amount has a 15% percent increase. Find the change and resulting amount.
Answer: change = 15/100 × 260 = 39; result = 299
08A 265 amount has a 20% markdown. Find the change and resulting amount.
Answer: change = 20/100 × 265 = 53; result = 212
Terminology
Words to know
- ratio
- A multiplicative comparison between two quantities.
- unit rate
- A rate expressed per one unit of the second quantity.
- equivalent ratios
- Ratios made by scaling both quantities by the same nonzero factor.
- constant of proportionality
- The unit rate k in a proportional equation y = kx.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Middle-school instructional guidance, mathematical practices, modeling, and coherent progression.Common Core State Standards for Mathematics — Grade 7
Grade-level expectations for ratios, number systems, algebra, geometry, statistics, and probability.Principles to Actions: Ensuring Mathematical Success for All
Research-informed emphasis on reasoning, representations, discourse, productive struggle, and conceptual understanding.