Desmos percent problems SAT: Solve percent equations fast

By the Cheetah Prep team · Reviewed July 13, 2026

For desmos percent problems sat, use Desmos to turn the percent into a multiplier, write one equation, then solve for the missing value. Skip the extra arithmetic. On the digital SAT, percent questions usually fit one of these structures: percent of, percent change, or reverse percent.

Here is the fast setup you can type directly into Desmos:

Percent of: “ $p\%$ of $A$ is $B$ ” becomes $B = A \cdot (p/100)$ .
Percent change sat: “ $A$ increased by $p\%$ to $B$ ” becomes $B = A \cdot (1 + p/100)$ . Decreased becomes $B = A \cdot (1 - p/100)$ .
Reverse percent: “After a $p\%$ decrease, the result is $B$ ” becomes $B = A \cdot (1 - p/100)$ , then solve for $A$ .

In Desmos, enter the equation and use a variable for the unknown, for example $B = A \cdot (1 + p/100)$ . Then solve. You can do it by entering values and asking for the unknown, or by graphing both sides and finding the intersection. If you want the general graphing approach for solving equations, start with the SAT Desmos guides and use the same “set two expressions equal and solve” idea on percent setups.

When to use this Desmos method

Use this Desmos method anytime an SAT problem describes a percent relationship in words and you need one unknown. Turn the percent into a multiplier, then write the equation.

Look for these common question patterns:

Percent of a quantity: The prompt uses words like “percent of,” “is,” “what is,” or “equals.”
Example pattern: “ $p\%$ of $A$ is $B$ .” One equation, one solve.
Percent change sat (increase or decrease): The prompt says “increased by,” “decreased by,” “grew,” “dropped,” “discount,” “tax,” “markup,” or “depreciated.”
Example pattern: “ $A$ increased by $p\%$ to $B$ .” Multiply by $1 + p/100$ or $1 - p/100$ , then solve for the missing value.
Reverse percent (original value): The prompt gives the final amount after a percent change and asks for the starting amount.
Example pattern: “After a $p\%$ decrease, the result is $B$ .” Solve $B = A \cdot (1 - p/100)$ for $A$ .

This approach is especially useful when:

The numbers are awkward, mental math is slow, and you are likely to slip.
The problem mixes words and algebra, and you want an equation you can check.
You want to check your setup fast by graphing both sides and using the intersection.

If you want a quick refresher on solving equations by graphing in Desmos, use the SAT Desmos guides.

Step by step in Desmos

Translate the words into one percent equation
Decide which structure you have, then write it as one equation.

Percent of: $B = A \cdot (p/100)$ .

Percent change sat: $B = A \cdot (1 + p/100)$ for an increase, or $B = A \cdot (1 - p/100)$ for a decrease.

Reverse percent: same equation as percent change, but the unknown is the original amount.
B=A*(1+p/100)
Type the equation with a single unknown
In Desmos, use one variable for the value you are solving for.

Example percent of setup: if $35\%$ of $x$ is $84$ , type $84 = x \cdot (35/100)$ .

Example percent change sat setup: if a price $x$ decreased by $18\%$ to $246$ , type $246 = x \cdot (1 - 18/100)$ .

Keep the percent as divided by $100$ so Desmos handles the decimal for you.
246=x*(1-18/100)
Solve by rewriting as an expression equal to zero
Desmos does not solve equations automatically in one line, so turn your equation into something that equals $0$ .

Take everything to one side. If you typed $246 = x \cdot (1 - 18/100)$ , you can instead type:

$x \cdot (1 - 18/100) - 246 = 0$ .

Now you are looking for the $x$ value where the expression hits $0$ .
x*(1-18/100)-246
Find the solution with the x intercept
After you graph the expression that equals $0$ , tap the graph to place a point on the curve.

Choose the option for the x intercept. Desmos will show the solution as the x coordinate of that intercept.

This works because the x intercept is where $y = 0$ , which matches your rewritten equation.
x*(35/100)-84
Alternate method: graph both sides and use the intersection
If you prefer to keep the original equation, graph the two sides as separate lines.

Type the left side as one line and the right side as another line.

Then tap the intersection point. The x coordinate of the intersection is the value that makes the two sides equal.
y=246 y=x*(1-18/100)
Quick check before you move on
Sanity check the direction and size.

If it is an increase, the multiplier $1 + p/100$ is greater than $1$ , so the final amount should be bigger than the original.

If it is a decrease, the multiplier $1 - p/100$ is less than $1$ , so the final amount should be smaller than the original.

If your solved value breaks that logic, your equation probably swapped the original and final values or used the wrong sign.

Exact expressions to enter

$B=A*(p/100)$ Type this into Desmos
Percent of. Use when the prompt says p percent of A is B.
$B=A*(1+p/100)$ Type this into Desmos
Percent change sat increase. Use when A increased by p percent to B.
$B=A*(1-p/100)$ Type this into Desmos
Percent change sat decrease. Use when A decreased by p percent to B.
$A=B/(1+p/100)$ Type this into Desmos
Reverse percent after an increase. Use when the final amount B is after a p percent increase and you need the original A.
$A=B/(1-p/100)$ Type this into Desmos
Reverse percent after a decrease. Use when the final amount B is after a p percent decrease and you need the original A.
$p=100*(B/A-1)$ Type this into Desmos
Find percent change when you know start A and end B, and the question asks for the percent increase or decrease.
$p=100*(1-B/A)$ Type this into Desmos
Find percent decrease when you know start A and end B, and the question specifically asks for percent decrease.
$B=A*(1+p/100)^t$ Type this into Desmos
Repeated percent change for t steps. Use when the same percent change happens each time period.
$A=B/(1+p/100)^t$ Type this into Desmos
Reverse repeated increase. Use when you know the final B after t increases of p percent and need the starting A.
$A=B/(1-p/100)^t$ Type this into Desmos
Reverse repeated decrease. Use when you know the final B after t decreases of p percent and need the starting A.

Worked SAT style example

Example

A jacket originally cost $x$ dollars. The store applies a 35% discount, then adds 8% sales tax to the discounted price. The final price is $56.70. What is$ x$?

Turn each percent change into a multiplier. A 35% discount means multiply by $1 - 35/100 = 0.65$ . An 8% tax means multiply by $1 + 8/100 = 1.08$ .
Write one equation for the final price: $56.70 = x(0.65)(1.08)$ .
In Desmos, type: y = 56.70 and y = x*0.65*1.08. Find the intersection x value, or type: 56.70 = x*0.65*1.08 and solve for x.
Solve: $x = 56.70/(0.65\cdot 1.08)$ . Desmos gives $x \approx 80.77$ .
Check the reasonableness: 35% off makes the price smaller, then 8% tax makes it a little bigger, so the original should be greater than $56.70$ , which matches $80.77$ .
If the question asks for the nearest cent, keep $x = 80.77$ dollars. If it asks for the nearest dollar, round to $81$ .

Answer:

x = 80.77

Common mistakes

Most wrong answers on desmos percent problems sat come from using the wrong multiplier or solving for the wrong variable.

Using $p$ instead of $p/100$ . If the problem says $15\%$ , the multiplier uses $15/100$ , not $15$ . In Desmos, type $(15/100)$ so you can see the conversion.
Mixing up “percent of” vs “percent change sat.”
“ $p\%$ of $A$ is $B$ ” is $B = A \cdot (p/100)$ .
“ $A$ increased by $p\%$ to $B$ ” is $B = A \cdot (1 + p/100)$ .
If you leave off the $1+$ or $1-$ , you are not modeling a change.
Reversing the direction of change. A decrease uses $1 - p/100$ , not $1 + p/100$ . A quick check: a decrease multiplier must be less than $1$ .
Solving for the final amount when the question wants the original. These are reverse percent problems, so you work backward. If $B = A \cdot (1 - p/100)$ and $B$ is given, solve for $A$ by dividing by the multiplier.
Entering an equation but never telling Desmos what is unknown. Use a variable (like $x$ ) for the missing value, then solve. If you graph, graph left and right separately, then find the intersection. If you need the general intersection workflow, see SAT Desmos guides.
Rounding too early. Keep exact inputs like $(17/100)$ and let Desmos carry the decimals until the end, then round only if the question asks.

When this method does not work

This Desmos setup stops being the fastest option when the problem is not one percent relationship with one unknown, or when the percent language is not a multiplier.

Here are the common situations where it wastes time or gives you the wrong setup:

More than one unknown: If both the percent and the original amount are unknown, you need a system, extra information, or answer choice testing. One equation will not do it.
Not actually a percent multiplier: Some questions say percent but are really about percentile, percent of a group, or a survey result. Those are reading problems, not algebra. If you cannot turn the sentence into $B = A \cdot \text{(multiplier)}$ , do not force it.
Percent change applied multiple times: Changes like “increase by $p\%$ , then decrease by $q\%$ ” can work in Desmos, but you must use two multipliers. Do not cancel them. Do not combine them into one percent unless the problem tells you to.
Constraints matter: Some word problems require a whole number, a maximum, or a minimum. Desmos might give a decimal intersection, but the SAT might want the nearest integer that actually makes sense in the situation.
Units and base value confusion: If the problem changes the base for “of what,” your equation can be wrong even if your algebra is right. Label what each variable stands for before you type anything.

If the main difficulty is isolating a variable after you set it up, use the algebra first approach from Desmos literal equations SAT: isolate a variable and check your work.

Practice questions

1.A jacket originally costs $85$ . It is discounted by $30\%$ , then sales tax of $8\%$ is added to the discounted price. What is the final price?

2.A population is $12{,}000$ and then increases by $15\%$ each year for 2 years. What is the population after 2 years?

3.After a $25\%$ decrease, a value becomes $180$ . What was the original value?

4.A store raises the price of an item by $20\%$ and then later reduces the new price by $20\%$ . The final price is $96$ . What was the original price?

5. $35\%$ of a number is $49$ . What is the number?

6.A quantity decreases from $250$ to $200$ . What is the percent change, rounded to the nearest percent?

FAQ

What is the fastest Desmos setup for desmos percent problems sat?

Turn the words into one equation with a percent multiplier. Use $p/100$ for percent of. Use $1 + p/100$ for an increase. Use $1 - p/100$ for a decrease. Then solve for the missing variable in Desmos.

How do I type percent change sat problems in Desmos without doing mental math?

Write it as a multiplier equation. For an increase: $B = A(1 + p/100)$ . For a decrease: $B = A(1 - p/100)$ . Plug in the numbers you know, use a variable for the unknown, then solve.

How do I find the original amount in a reverse percent problem?

Treat the final amount as the original multiplied by a change factor. For a decrease, use $B = A(1 - p/100)$ . For an increase, use $B = A(1 + p/100)$ . Solve the equation for $A$ .

Should I convert the percent to a decimal or keep it as $p/100$?

Keep it as $p/100$ . It prevents conversion mistakes. Desmos does the division for you. Simplify later if you want.

What do I do if the problem says, percent more than or percent less than?

Percent more than means multiply by $1 + p/100$ . Percent less than means multiply by $1 - p/100$ . The percent is measured from the original amount, so start with that original and apply the multiplier.

How can I use Desmos to check that my percent equation matches the story?

After you write the equation, sanity check it with an easy value. For example, if $p = 0$ , an increase or decrease setup should give $B = A$ . If $p = 100$ and it is an increase, it should double. If it is a decrease, it should go to $0$ .

When should I avoid Desmos for percent problems?

If the numbers are simple and the question is clearly asking for a quick fraction or mental math result, Desmos can slow you down. If the question only asks you to interpret a statement about percent, skip the equation.

What is the most common mistake with Desmos percent problems sat?

Using $p$ instead of $p/100$ , or adding $p$ instead of multiplying by $1 + p/100$ or $1 - p/100$ . Percent change scales the original amount, so you multiply instead of add.

About this page: written and reviewed by the Cheetah Prep team. Last reviewed July 13, 2026.