SAT Percent Word Problems: Name the Amount the Percent Describes

In a percent equation, the percent belongs to one specific amount. Write that amount down before you multiply. For a rate $r$ written as a decimal, an increase of that amount uses the factor $1+r$, and a decrease uses the factor $1-r$. If a positive rate $r$ increases an amount and the same rate then decreases the result, the combined factor is $(1+r)(1-r)=1-r^{2}$. Whenever $0<r<1$, that product is less than $1$, so the final amount is smaller than the amount you started with.

College Board’s SAT Math overview lists Problem-Solving and Data Analysis among the four math areas and says approximately 30% of Math section questions are set in context. In the Student Question Bank, the percentages skill in that area includes discounts, interest, taxes, and tips, and the relationship between a percent increase or decrease and a growth factor. OpenStax Elementary Algebra finds a percent increase or a percent decrease by dividing the change by the original amount. The ticket, hoodie, fund, and yearbook examples below are original Kibo practice.

Match each phrase with its factor

A campus club sells a concert ticket for $\$40$. The processing charge is $6\%$ of the ticket price. The $6\%$ describes the $\$40$ ticket, so the charge is $0.06\times 40=2.40$ dollars. The total is $40+2.40=42.40$ dollars, which is the same as $40\times 1.06$. The $1$ in $1.06$ keeps the ticket price, and the $0.06$ adds the charge.

The factor $1.06$ is the growth factor for a $6\%$ increase of the ticket price. $1-0.06=0.94$, so a $6\%$ decrease of the same $\$40$ ticket gives $40\times 0.94=37.60$ dollars.

Divide when the starting price is the unknown

After a $25\%$ increase, a club hoodie costs $\$45$. Let $P$ be the price in dollars before the increase. The $25\%$ describes $P$, so

$$1.25P=45$$

$$P=\frac{45}{1.25}=36$$

The price before the increase was $\$36$. From the definition of a $25\%$ increase, $36\times 0.25=9$ and $36+9=45$. The factor check is $36\times 1.25=45$.

Two calculations that start from $\$45$ answer different questions. $45\times 1.25=56.25$ adds $25\%$ of the new price. $45\times 0.75=33.75$ subtracts $25\%$ of the new price. The price before a $25\%$ increase is the new price divided by $1.25$.

The linear-equation guide shows how to apply one operation to both sides while you isolate an unknown. The PSAT percent-change guide recovers a price after a discount. The same reference idea applies here when the starting amount of an increase is the unknown.

The same rate up and down leaves a smaller amount

A club fund holds $\$500$. The balance increases by $10\%$, and then it decreases by $10\%$.

• The increase uses $\$500$: $500\times 1.10=550$. It adds $500\times 0.10=50$ dollars.
• The decrease uses $\$550$: $550\times 0.90=495$. It removes $550\times 0.10=55$ dollars.
• Together, $500\times 1.10\times 0.90=495$.

For a rate $r$ with $0<r<1$,

$$(1+r)(1-r)=1-r^{2}$$

Here $r=0.10$, so the product is $1-0.01=0.99$, and $500\times 0.99=495$. The fund finishes $500\times 0.01=5$ dollars below its start. The decrease removes $\$55$, while the increase added $\$50$, because the decrease uses the larger intermediate balance.

These two factors can be multiplied in either order. A $10\%$ decrease first gives $500\times 0.90=450$, and the following $10\%$ increase gives $450\times 1.10=495$. The intermediate balances are $\$450$ and $\$550$. The ending balance is $\$495$ on both paths.

A growth factor applied over several equal periods follows a different model. The exponential-growth guide separates that repeated factor from a single percent change.

Give each percent its own amount

A yearbook lists for $\$80$. The sale price is $20\%$ less than the list price. Shipping is $5\%$ of the sale price.

1. The sale price uses the list price: $80\times 0.80=64$ dollars.
2. Shipping uses the sale price: $64\times 0.05=3.20$ dollars.
3. The total is $64+3.20=67.20$ dollars.

One product gives the same total: $80\times 0.80\times 1.05=80\times 0.84=67.20$. The $20\%$ describes the $\$80$ list price, and the $5\%$ describes the $\$64$ sale price.

Adding $5\%$ of the list price gives $64+4=68$. Subtracting the rates, $20\%-5\%=15\%$, and $15\%$ off the list price is $80\times 0.85=68$. Both of those results use the list price for every percent. The stated shipping rule uses the sale price, so the total is $\$67.20$.

Try four original practice questions

Exactly one choice answers each question. The only charges are the ones named in the question.

1. A notebook costs $\$25$. A sleeve for it costs $8\%$ of the notebook price. Which equation gives the total cost $T$ in dollars?

   • A. $T=25+8$
   • B. $T=0.08\times 25$
   • C. $T=25\times 1.08$
   • D. $T=25+0.08$

2. After a $20\%$ increase, a jacket costs $\$54$. What was the price before the increase?

   • A. $\$43.20$
   • B. $\$45.00$
   • C. $\$64.80$
   • D. $\$34.00$

3. A concession stand has $250$ bottles of water. The count increases by $20\%$, then decreases by $20\%$. How many bottles are there at the end?

   • A. $250$
   • B. $240$
   • C. $200$
   • D. $300$

4. A yearbook lists for $\$60$. The sale price is $25\%$ less than the list price, and shipping is $8\%$ of the sale price. What is the total?

   • A. $\$45.00$
   • B. $\$48.60$
   • C. $\$49.80$
   • D. $\$64.80$

Underline the amount, then write the factor

• Copy the phrase that contains the percent and underline the amount it describes.
• Use $1+r$ for an increase of that amount and $1-r$ for a decrease of that amount.
• When the result is known and the starting amount is unknown, divide by the factor.
• For two percents, update the reference after the first change, then apply the second factor.
• Substitute the result into the original sentence.

If a result misses, record whether the reference, the factor, or the arithmetic needs another look. The practice error log keeps that note for a later recheck.

Try a free SAT practice question with Kibo and name the amount your percent describes before you calculate.

Prepared with AI assistance. The ticket totals, hoodie price, fund balances, yearbook totals, and every practice choice were checked with separate exact arithmetic. No human review or score improvement is claimed. Sources checked November 15, 2026. SAT is a registered trademark of College Board, which is not affiliated with or endorsing this guide.