Learn with Amar
Teaching video
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Grade 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to work backward from a discounted amount.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Percent multipliers and one-step equations.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
A fictional art kit costs $42 after a 30% discount. What was the price before the discount?
Why this math matters
A discounted price is a fraction of the original, so reverse percentages require division by the remaining fraction. Use a multiplier equation to recover original dimensions, populations, or prices from a percentage change.
Set up the model
A useful answer starts with clear assumptions:
- The discount applies once to the original price.
- There are no other charges in this example.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Work backward from a discounted amount
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A fictional art kit costs $42 after a 30% discount. What was the price before the discount?
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the quantities
remaining fraction = 1 − 0.30 = 0.70
A 30% discount leaves 70% of the original amount.
Apply the relationship
0.70p = 42; p = 42/0.70
Divide the known final amount by the retained fraction.
Check and interpret
p = $60; 60 − 0.30(60) = $42
The forward calculation confirms the recovered original price.
The result
p = $60; 60 − 0.30(60) = $42
The forward calculation confirms the recovered original price.
Common mistakes to catch
- Adding 30% of the discounted price uses the wrong base.
- A decrease of 30% uses a multiplier of 0.70, not 0.30.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
A quantity is 72 after a 20% decrease. Find its original value.
Show a hint
The final amount is 80% of the original.
Reveal answer and explanation
90
72/0.80 = 90.
Practice 2
A quantity is 96 after a 20% increase. Find its original value.
Show a hint
An increase retains 120%, not 80%.
Reveal answer and explanation
80
96/1.20 = 80, and 80 + 16 = 96.
Take the idea with you
Use a multiplier equation to recover original dimensions, populations, or prices from a percentage change.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Match time units in simple interest
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