Card 1 of 20
EasyStudy card 1
Prompt
What multiplier gives a price after a \(d\%\) discount?
Use the fraction of price remaining.
Answer
\(1-d/100\).
Example
A \(30\%\) discount uses \(0.70\).
MathChapter 7: Percents
Flashcards
Percent Word Problems Flashcards
Twenty concise cards on price adjustments, mixtures, investments, nested percentages, and modeling traps.
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Card 2 of 20
EasyStudy card 2
Prompt
What multiplier gives a total after \(t\%\) tax?
Tax is added to the base price.
Answer
\(1+t/100\).
Example
An \(8\%\) tax uses \(1.08\).
Card 3 of 20
EasyStudy card 3
Prompt
How is a markup applied to wholesale cost?
Markup is an increase from cost.
Answer
Multiply cost by \(1+m/100\).
Example
A \(25\%\) markup on \(\$80\) gives \(\$100\).
Card 4 of 20
EasyStudy card 4
Prompt
How is a tip or gratuity amount calculated?
This finds the tip, not the total.
Answer
Multiply the bill subtotal by the decimal tip rate.
Example
\(0.18(\$50)=\$9\).
Card 5 of 20
EasyStudy card 5
Prompt
How is a bill total found after a tip?
Include the original subtotal.
Answer
Multiply the subtotal by one plus the decimal tip rate.
Example
\(\$50(1.18)=\$59\).
Card 6 of 20
MediumStudy card 6
Prompt
How do you find an original price from a sale price?
Reverse the discount operation.
Answer
Divide the sale price by the remaining-price multiplier.
Example
After \(20\%\) off, \(\$72/0.80=\$90\).
Card 7 of 20
MediumStudy card 7
Prompt
How do you find a pretax amount from a taxed total?
Do not subtract the tax rate as dollars.
Answer
Divide the total by the tax multiplier.
Example
With \(8\%\) tax, \(\$108/1.08=\$100\).
Card 8 of 20
MediumStudy card 8
Prompt
How should a discount followed by tax be modeled?
Tax applies to the discounted price.
Answer
Multiply the original price by both factors in order.
Example
\(P(0.80)(1.10)=0.88P\).
Card 9 of 20
MediumStudy card 9
Prompt
What quantity is conserved in a mixture problem?
Add the pure amounts contributed by each solution.
Answer
The total amount of pure ingredient.
Example
\(0.20(2)+0.50(3)=1.9\) liters of ingredient.
Card 10 of 20
MediumStudy card 10
Prompt
What is the basic two-solution mixture equation?
Rate times volume gives pure amount.
Answer
\(r_1v_1+r_2v_2=r_f(v_1+v_2)\).
Example
\(0.20(2)+0.50(3)=0.38(5)\).
Card 11 of 20
MediumStudy card 11
Prompt
Why should unequal mixture concentrations not be simply averaged?
Use a weighted average through pure amounts.
Answer
Their solution amounts may have different weights.
Example
\(1\) liter and \(9\) liters do not contribute equally.
Card 12 of 20
MediumStudy card 12
Prompt
In a two-account investment problem, how are the principal amounts related?
If one amount is \(x\), the other is \(T-x\).
Answer
They add to the total invested principal.
Example
For total \(\$10{,}000\), use \(x\) and \(10{,}000-x\).
Card 13 of 20
MediumStudy card 13
Prompt
What is the simple-interest allocation equation for one year?
Add interest from both accounts.
Answer
\(r_1x+r_2(T-x)=I\).
Example
\(0.03x+0.07(10{,}000-x)=540\).
Card 14 of 20
MediumStudy card 14
Prompt
What common investment mistake double-counts principal?
Each rate applies only to its allocated portion.
Answer
Applying each interest rate to the entire total.
Example
Use \(x\) and \(T-x\), not \(T\) twice.
Card 15 of 20
MediumStudy card 15
Prompt
How do you find a percent of a subgroup?
The subgroup becomes the second whole.
Answer
Multiply the full amount by the first rate and then the subgroup rate.
Example
\(800(0.35)(0.40)=112\).
Card 16 of 20
MediumStudy card 16
Prompt
What is the overall rate when \(a\%\) are in a group and \(b\%\) of that group qualify?
Nested ‘of’ relationships multiply.
Answer
\((a/100)(b/100)\) in decimal form.
Example
\(60\%\) of \(35\%\) gives \(21\%\) overall.
Card 17 of 20
MediumStudy card 17
Prompt
How should repeated removals be modeled?
Each later percent uses the current remainder.
Answer
Multiply the fractions remaining after every removal.
Example
Removing \(30\%\), then \(20\%\), leaves \(0.70(0.80)=56\%\).
Card 18 of 20
HardStudy card 18
Prompt
Why cannot a discount and tax usually be combined by subtracting their rates?
The second adjustment acts on the changed price.
Answer
They use different bases and therefore require separate multipliers.
Example
A \(20\%\) discount then \(10\%\) tax gives \(0.88\), not \(0.90\).
Card 19 of 20
HardStudy card 19
Prompt
How can the required amount of a new mixture solution be modeled?
Use both pure-amount and total-volume changes.
Answer
Let its amount be \(x\) and equate initial plus added pure ingredient to final pure ingredient.
Example
\(0.20(6)+0.70x=0.50(6+x)\).
Card 20 of 20
HardStudy card 20
Prompt
What is a reliable SAT strategy for a complex percent word problem?
One rate can use a different whole from the next.
Answer
Label each percent's base, write multipliers or a conservation equation, and estimate before calculating.
Example
For discount then tax, label original price, sale price, and taxed total separately.
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