Percentage Change Word Problem 1 Calculator takes a before-and-after scenario written in plain language and maps it onto the percent change formula. Enter the starting amount and the ending amount from the scenario, and the tool substitutes both values into P = ((Y − X) / X) × 100 with every step shown.
Turn a word problem into two numbers
Word problems about percentage change describe a quantity at two points in time: a rent before an increase and after it, an inventory count before and after a sale, a population before and after a year of growth.
The first task is always extraction, not calculation: pull the original value and the new value out of the sentence, and set aside anything else, such as a stated dollar amount or population count that is not the two comparison figures.
Worked example: a rent increase
A tenant's monthly rent moves from $1,150 to $1,242.20. To find the percentage increase, subtract the old rent from the new rent: 1242.20 − 1150 = 92.20. Divide that difference by the original rent: 92.20 / 1150 = 0.08. Multiply by 100 to express it as a percent: 8 percent.
Percentage Change Word Problem 1 Calculator performs exactly these three steps and reports 8 percent as the answer, with the intermediate division shown so the work can be checked line by line.
Worked example: a declining count
A warehouse holds 640 units at the start of a quarter and 512 units at the end. The change is 512 − 640 = −128. Dividing by the original count gives −128 / 640 = −0.20. Multiplying by 100 gives −20 percent.
The negative sign here is not an error; it correctly reports a 20 percent decrease in inventory over the quarter.
Check the reasonableness of the answer
A quick sanity check catches most extraction mistakes: is the new value roughly what you would expect from the reported percent? An 8 percent increase on $1,150 should land near $1,242, and it does. A 20 percent decrease from 640 should land near 512, and it does.
When the check does not roughly match, the original or new value was probably swapped, or a value from elsewhere in the word problem was used instead of the comparison figures.
Avoid this common mistake
The most common error in percentage word problems is using the wrong number as the denominator, often because the sentence structure buries the "original" value in the middle of a paragraph rather than stating it first.
Percentage Change Word Problem 1 Calculator always divides by the value you mark as the starting amount, so double-check which figure the word problem describes as happening first in time before entering it.
Worked example: tuition with an explicit increase amount
Some word problems state the change amount directly rather than the ending value. "Tuition was $12,000 and increased by $960" requires one extra step before the percent formula applies: add the increase to the original to find the new total, 12,000 + 960 = 12,960, then compute (12,960 − 12,000) / 12,000 × 100, which is 8 percent.
Percentage Change Word Problem 1 Calculator accepts either form, the ending value directly or the original plus a stated change, and performs this addition automatically when the change amount is entered instead of the new total.
Practice identifying the two key numbers
Reading comprehension, not arithmetic, is the actual skill being tested in most percentage word problems.
Circle or underline every number in the sentence, then ask which one describes the situation "before" and which describes it "after." Numbers that describe a rate, a percent already stated, or an unrelated quantity like a population size used only for context should be set aside.
Once the before-and-after pair is correctly identified, the calculation itself is always the same three-step process: subtract, divide, multiply by 100.
Frequently asked questions
How do you solve a percentage word problem?
To solve a percentage word problem, first identify the original value and the new value described in the sentence, then apply P = ((New − Original) / Original) × 100. Extraction of the correct two numbers is usually the harder step, not the arithmetic itself.
What is the formula for a percentage increase word problem?
The formula for a percentage increase word problem is the same percent change formula, P = ((New − Original) / Original) × 100, with a positive result confirming an increase. If the word problem states the increase amount directly rather than the new total, add that amount to the original value first to get New.
How do you find the original amount in a percentage word problem?
To find the original amount when the new amount and the percent change are known, divide the new amount by (1 + P/100) for an increase or by (1 − P/100) for a decrease. A price of $135 after a 12.5 percent increase means the original was 135 / 1.125, which is $120.
What if the word problem gives a percent decrease?
When the word problem gives a percent decrease, applying it produces a negative P in the percent change formula, and the resulting new value is smaller than the original. Percentage Change Word Problem 1 Calculator reports decreases as negative percentages consistently, matching the sign convention used across every percent-based tool on this site.
Why does my answer not match the textbook answer?
An answer mismatch with a textbook usually traces to a rounding difference or to using the wrong reference value as the denominator. Recompute using the value the problem describes first in time as the original amount, and compare intermediate steps rather than only the final percent.
What if the word problem gives the change amount instead of the new total?
If the word problem gives the change amount instead of the new total, add the change to the original value first to find the new total, then apply the standard percent change formula to those two figures.
What is the percent increase if tuition of $12,000 rises by $960?
The percent increase is 8 percent, found by adding 960 to 12,000 to get a new total of 12,960, then computing (12,960 − 12,000) / 12,000 × 100.
Summary
Percentage Change Word Problem 1 Calculator extracts an original value and a new value from a text scenario and runs them through P = ((New − Original) / Original) × 100, printing the subtraction, the division, and the final percent as separate steps.
The tool handles both rising and falling scenarios, reporting increases as positive percentages and decreases as negative ones, matching the direction of the underlying change.