Calculate Percent Change - TEAS Mathematics

An investment account declined from $\$7{,}200$ to $\$6{,}840$ . What percent loss did the account experience?
Answer: 5\% When you encounter percent change problems, you're calculating how much a quantity has changed relative to its original value. The key formula is: percent change = (change in value ÷ original value) × 100%. To find the percent loss, first calculate the actual dollar amount lost: $\$7{,}200 - \$6{,}840 = \$360$ . This $360 represents the decline in the account's value. Next, divide this loss by the original amount: $\$360 ÷ \$7{,}200 = 0.05$ . Converting to a percentage: $0.05 × 100\% = 5\%$ . This confirms answer choice B is correct. Looking at the wrong answers: Choice A (4%) would result from incorrectly calculating the dollar loss as $288 instead of $360. Choice C (6%) might come from rounding errors or miscalculating the division. Choice D (8%) could result from using the wrong denominator—perhaps dividing by the final value ($ $\$6{,}840$ $) instead of the original value, or from calculation errors. The most common trap in percent change problems is using the wrong denominator. Always remember that percent change uses the original value as the base, not the final value. Also, double-check your subtraction to ensure you're finding the correct dollar amount of change. On the TEAS, percent problems often test whether you can identify the correct reference point—the "of what" in percentage calculations.
The temperature in a laboratory increased from $68^{\circ}\text{F}$ to $86^{\circ}\text{F}$ . What was the percent increase, rounded to the nearest whole percent?
Answer: 26\% Percent increase problems test your ability to calculate how much a quantity has grown relative to its original value. When you see temperature changes or any "from X to Y" scenario, you're looking at a percent change calculation. To find percent increase, you need the formula: $\text{Percent Increase} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100$ Here, the temperature increased from $68°F$ to $86°F$ . The change is $86 - 68 = 18°F$ . Now divide this change by the original temperature: $\frac{18}{68} = 0.2647$ . Converting to a percentage: $0.2647 \times 100 = 26.47\%$ . Rounded to the nearest whole percent, this gives us 26%, which is answer choice B. Looking at the wrong answers: A) 21% would result from calculation errors, possibly rounding too early or using incorrect values. C) 31% might come from accidentally using the new value (86) as the denominator instead of the original value (68). D) 36% is too high and likely results from more significant computational mistakes or formula confusion. The key trap here is using the wrong denominator. Always remember that percent increase uses the original value as your reference point, not the new value or the average of both. Practice identifying which number represents your "original" or starting value—it's typically the first number mentioned or the "from" value in word problems.
Use the chart to answer the question. What percent increase in fuel efficiency did the sedan experience?
Answer: 13.30% Increase $=30.6-27.0=3.6\text{ mpg}.$ Percent increase $=\dfrac{3.6}{27.0}\times100=13.3\%.$ A: Divides by 30.6. C & D: Result from using 4 or 4.8 mpg as the difference.
A container's mass fell from $1.20\text{ kg}$ to $1.05\text{ kg}$ after some material was removed. What percent decrease in mass occurred?
Answer: 12.5\% When you encounter percent change problems, you're working with the formula: percent change = $\frac{\text{change in value}}{\text{original value}} \times 100\%$ . The key is identifying what decreased and what you're comparing it to. Here, the container's mass decreased from 1.20 kg to 1.05 kg. First, find the change: $1.20 - 1.05 = 0.15 \text{ kg}$ . Then divide this change by the original mass: $\frac{0.15}{1.20} = 0.125 = 12.5\%$ . Looking at the wrong answers: Choice A (10.0%) likely comes from incorrectly using 1.05 kg as the denominator instead of the original 1.20 kg, or from rounding errors. Choice C (14.3%) might result from dividing the change by the final mass ( $\frac{0.15}{1.05} ≈ 0.143$ ), which is a common mistake—you must always use the original value as your reference point. Choice D (16.7%) could come from calculation errors or misunderstanding the relationship between the values. The correct answer is B (12.5%) because $\frac{0.15}{1.20} \times 100\% = 12.5\%$ . Study tip: For percent decrease problems on the TEAS, always use the original (starting) value in the denominator, never the final value. A helpful memory device: "percent change starts with the start"—meaning your calculation should reference where you started from, not where you ended up.
A town's population was 10,000 in 2018. It increased by 10% from 2018 to 2019. From 2019 to 2020, it increased by a number of people equal to 15% of the 2018 population. What was the percent increase in population from 2019 to 2020? (Round to the nearest tenth of a percent)
Answer: 13.6% First, find the 2019 population. An increase of 10% on 10,000 is 1,000, so the 2019 population was $10,000 + 1,000 = 11,000$ . Next, find the population increase from 2019 to 2020. This increase was 15% of the 2018 population: $0.15 \times 10,000 = 1,500$ . The question asks for the percent increase from 2019 to 2020. The base for this calculation is the 2019 population (11,000), and the change is 1,500. Percent increase = $\frac{1,500}{11,000} \times 100\% \approx 0.13636... \times 100\% \approx 13.6\%$ . A is incorrect because it uses the stated 15% value directly, failing to recognize that the base population for the percentage calculation changed from 2018 to 2019. C is incorrect because it uses the final 2020 population (12,500) as the base: $1,500/12,500 = 12.0\%$ . D is incorrect because it calculates the total percent change from 2018 to 2020: $(2,500/10,000) = 25.0\%$ .
A retail item's price was increased by 25%. A week later, the new price was decreased by 25%. What was the total percent change in the item's price from its original price to its final price?
Answer: A 6.25% decrease Let the original price be P. An increase of 25% results in a new price of $P \times (1 + 0.25) = 1.25P$ . Then, a 25% decrease is applied to this new price: $1.25P \times (1 - 0.25) = 1.25P \times 0.75 = 0.9375P$ . To find the total percent change, compare the final price (0.9375P) to the original price (P). The change is $0.9375P - P = -0.0625P$ . The percent change is $\frac{-0.0625P}{P} \times 100\% = -6.25\%$ . This represents a 6.25% decrease. A is incorrect because it results from the common mistake of assuming that a 25% increase and a 25% decrease cancel each other out. C is incorrect and represents a plausible but unsubstantiated guess. D is incorrect because it correctly calculates the magnitude of the change but has the wrong sign (increase instead of decrease).
A patient's weight decreased from 200 pounds to 160 pounds. Later, the patient regained some weight, and the percent increase from their lowest weight was half of the initial percent decrease. What was the patient's final weight?
Answer: 176 pounds First, calculate the initial percent decrease. The original weight was 200 lb, and the new weight was 160 lb. The change was $160 - 200 = -40$ lb. The percent decrease is $\frac{|-40|}{200} \times 100\% = \frac{40}{200} \times 100\% = 20\%$ . Next, the patient regained weight. The percent increase from their lowest weight (160 lb) was half of the initial percent decrease. Half of 20% is 10%. So, the weight increased by 10% from 160 lb. The weight gain is $160 \times 0.10 = 16$ lb. The final weight is $160 + 16 = 176$ pounds. B is incorrect and results from assuming the patient regained half the weight in pounds (20 lb), not half the percent decrease. C is incorrect and may result from miscalculating the initial percent decrease as 25% (40/160) and then taking half of that (12.5%) to calculate the increase: $160 \times 1.125 = 180$ . Oh, that's B. Let's re-evaluate. 40/160=25%. Half is 12.5%. 160*1.125 = 180. My distractor B rationale was wrong. B is from $40/160 = 25\%$ , half is 12.5%, $160*1.125 = 180$ . So B is a very strong distractor. My initial rationale for B was $160 + (40/2)) = 180$ . So it's doubly strong. Let's find a rationale for C. Maybe 20% of 160 is 32. Half is 16. That leads to the correct answer. How about 184? Maybe $200*0.92$ ? No. Let's say C is a plausible guess or calculation error. D is incorrect because it implies a 15% weight gain, which would be half the weight loss in pounds (20) plus the original percent decrease (20%). No, $160 \times 1.1875 = 190$ . 18.75%? Not obvious how one would get this.
During a sale, a jacket's price fell from $59.99 to $47.99. What percent discount was offered, rounded to the nearest whole percent?
Answer: 20\% off When you encounter percent discount problems, you're calculating how much the price decreased as a percentage of the original price. The key formula is: percent discount = (original price - sale price) ÷ original price × 100%. Let's work through this step-by-step. The jacket's original price was $59.99, and the sale price is $47.99. First, find the dollar amount of the discount: $59.99 - $47.99 = $12.00. Next, divide this discount by the original price: $12.00 ÷ $59.99 = 0.2000... Converting to a percentage: 0.2000 × 100% = 20.00%. Rounded to the nearest whole percent, this is 20%. Looking at the wrong answers: Choice A (17%) likely comes from incorrectly using the sale price as the denominator instead of the original price, or from calculation errors. Choice C (23%) might result from rounding errors or misplacing decimal points during calculation. Choice D (25%) is a common trap answer because $12 is exactly 25% of $48, and students sometimes approximate $59.99 as $48 instead of treating it as essentially $60. The correct answer is B) 20% off. Remember this key strategy for discount problems: always divide the discount amount by the original price, not the sale price. Also, when dealing with prices like $59.99, it's often helpful to round to $60 for quick estimation—in this case, $12 ÷ $60 gives you exactly 20%, confirming your precise calculation.
A clothing store buys a jacket for $80. They mark it up by 75% to set the initial selling price. The jacket is then put on sale for 20% off, and a week later an additional 10% is taken off the sale price. What is the percent change from the store's original cost to the final selling price of the jacket?
Answer: A 26% increase First, calculate the initial selling price: $\$80 \times (1 + 0.75) = \$80 \times 1.75 = \$140$ . Next, apply the first 20% discount: $\$140 \times (1 - 0.20) = \$140 \times 0.80 = \$112$ . Then, apply the additional 10% discount to the new sale price: $\$112 \times (1 - 0.10) = \$112 \times 0.90 = \$100.80$ . This is the final selling price. Finally, calculate the percent change from the original cost ($80) to the final price ($100.80). The change in price is $\$100.80 - \$80 = \$20.80$ . The percent change is $\frac{\$20.80}{\$80} \times 100\% = 0.26 \times 100\% = 26\%$ . A is incorrect and results from simply adding and subtracting the percentages: 75% - 20% - 10% = 45%. B is incorrect and represents the percent profit after only the first discount, not the second. C is incorrect and represents the total combined discount percentage (28%) from the marked-up price, not the percent change from the original cost.
A factory reduced its annual energy use from 1.20 million kWh to 0.93 million kWh. What percent decrease is this?
Answer: 22.5\% When you encounter percent decrease problems, you're calculating how much a quantity has dropped relative to its original value. The key formula is: percent decrease = (original value - new value) ÷ original value × 100%. Let's work through this step by step. The factory's energy use dropped from 1.20 million kWh to 0.93 million kWh. First, find the actual decrease: 1.20 - 0.93 = 0.27 million kWh. Next, divide this decrease by the original amount: 0.27 ÷ 1.20 = 0.225. Finally, convert to a percentage: 0.225 × 100% = 22.5%. Looking at the wrong answers: Choice A (18.5%) likely comes from calculation errors or possibly confusing the decrease with an increase calculation. Choice B (20.0%) might result from rounding errors or approximating too early in the calculation. Choice D (24.0%) could stem from dividing the decrease by the new value instead of the original value (0.27 ÷ 0.93 ≈ 0.29 or 29%, though that's still not exactly 24%). The correct answer is C (22.5%). Remember this key point: always divide by the original value, not the new value, when calculating percent change. A helpful way to check your work is to verify that 22.5% of 1.20 equals 0.27 (the decrease), and 1.20 - 0.27 = 0.93 (the final amount). This backward check can catch calculation mistakes on the TEAS.
A stock's price fell from $32.00 to $29.12. What percent decrease is this, to the nearest tenth of a percent?
Answer: 9.0\% When you encounter percent change problems, you're working with the fundamental concept of comparing an original value to a new value. The key formula is: percent change = $\frac{\text{change in value}}{\text{original value}} \times 100\%$ . For decreases, the result will be negative, but we typically report it as a positive "percent decrease." Let's calculate this step by step. The stock fell from $32.00 to $29.12, so the change in value is $29.12 - 32.00 = -\$2.88$ . The decrease amount is $2.88. Now apply the formula: $\frac{2.88}{32.00} \times 100\% = 0.09 \times 100\% = 9.0\%$ . This confirms answer C is correct. Looking at the wrong answers: A) 6.3% is too small and might result from using the wrong denominator or making a calculation error. B) 7.5% is also too low and could come from rounding errors or computational mistakes. D) 10.2% is too high and might result from using $29.12 as the denominator instead of the original price of $32.00. The most common trap in percent change problems is using the wrong value as your denominator. Always remember that percent change is calculated using the original value as your base, not the new value. Double-check your arithmetic, and when the problem asks for rounding "to the nearest tenth," make sure your final answer reflects that precision.
The price of a paperback novel rose from $24.50 to $28.00. What was the percent increase in the price of the book, to the nearest tenth of a percent?
Answer: 14.3\% Percent increase questions test your ability to calculate how much a value has grown relative to its original amount. When you see a price change problem, you need to find the difference between the new and old values, then express that difference as a percentage of the original value. To find the percent increase, use the formula: $\frac{\text{new value} - \text{original value}}{\text{original value}} \times 100\%$ Here, the original price was $24.50 and the new price is $28.00. The increase is $28.00 - $24.50 = $3.50. Now divide this increase by the original price: $\frac{3.50}{24.50} = 0.1429$ . Converting to a percentage: $0.1429 \times 100\% = 14.29\%$ , which rounds to 14.3%. Looking at the wrong answers: Choice A (12.8%) likely comes from incorrectly using the new price as the denominator instead of the original price. Choice C (16.5%) and Choice D (17.8%) represent calculation errors, possibly from misplacing decimal points or using incorrect formulas. These higher percentages might also result from confusing percent increase with other percentage calculations. The correct answer is B (14.3%). Remember this key pattern: for percent increase problems, always divide the change by the original value, not the new value. The original value is your reference point for measuring growth. Also, pay attention to rounding instructions - "to the nearest tenth" means one decimal place.
A student's exam score dropped from 88 to 79. What is the percent decrease in the score, to the nearest tenth of a percent?
Answer: 10.2\% Percent decrease problems test your ability to calculate how much a value has declined relative to its original amount. When you see "percent decrease," remember that you're always comparing the change to the original value, not the new value. To find percent decrease, use this formula: $\text{Percent decrease} = \frac{\text{original value - new value}}{\text{original value}} \times 100\%$ Here, the original score was 88 and the new score is 79. The decrease is $88 - 79 = 9$ points. Now calculate: $\frac{9}{88} \times 100\% = 0.1023... \times 100\% = 10.23...\%$ Rounded to the nearest tenth, this gives us 10.2%, which is answer choice B. Let's examine why the other answers are incorrect. Choice A (9.1%) likely comes from incorrectly dividing the point decrease by 100 instead of using the proper percentage formula. Choice C (11.4%) might result from dividing the change by the new value (79) instead of the original value (88) — a common mistake that reverses the reference point. Choice D (12.7%) appears to involve calculation errors, possibly combining multiple mistakes in the formula application. The key strategy here is remembering that percent decrease always uses the original value as the denominator, never the final value. Also, don't forget to round properly — the TEAS often tests whether you can follow rounding instructions precisely. Practice these percentage problems until the formula becomes automatic.
A river's water level rose from $3.4\text{ m}$ to $4.5\text{ m}$ after heavy rain. What was the percent increase, to the nearest tenth of a percent?
Answer: 32.4\% Percent increase problems test your ability to calculate how much a quantity has grown relative to its original value. When you see questions about changes in measurements like water levels, temperatures, or populations, think about the relationship between the change and the starting point. To find percent increase, you need the formula: $\text{Percent increase} = \frac{\text{new value} - \text{original value}}{\text{original value}} \times 100\%$ The water level rose from $3.4\text{ m}$ to $4.5\text{ m}$ . First, find the actual increase: $4.5 - 3.4 = 1.1\text{ m}$ . Then divide this change by the original value: $\frac{1.1}{3.4} = 0.3235...$ Converting to a percentage: $0.3235... \times 100\% = 32.35...\%$ , which rounds to $32.4\%$ . Choice A (23.5%) likely comes from incorrectly using the new value as the denominator: $\frac{1.1}{4.5} \times 100\% \approx 24.4\%$ , then rounding or calculation errors. Choice B (29.4%) might result from arithmetic mistakes in the division or confusion about which values to use. Choice D (34.9%) could come from rounding errors or miscalculating the original increase amount. Remember that percent increase always uses the original value as your reference point in the denominator, not the final value. A helpful check: if something increases by about one-third of its original size (1.1 is roughly one-third of 3.4), expect an answer around 33%.
After a fitness program, a person's weight fell from 185 lb to 171 lb. What was the percent decrease, to the nearest tenth of a percent?
Answer: 7.6\% Percent decrease problems test your ability to calculate how much a value has dropped relative to its original amount. When you see questions about weight loss, price reductions, or any situation where a quantity gets smaller, you're looking at percent decrease. To find percent decrease, you need the formula: $\text{Percent decrease} = \frac{\text{original value} - \text{new value}}{\text{original value}} \times 100\%$ Here, the original weight is 185 lb and the new weight is 171 lb. The decrease is $185 - 171 = 14$ lb. Now calculate: $\frac{14}{185} \times 100\% = 0.0757... \times 100\% = 7.57...\%$ Rounded to the nearest tenth, this gives us 7.6%, which is answer choice B. Looking at the wrong answers: Choice A (6.5%) likely comes from calculation errors or rounding too early in the process. Choice C (8.8%) might result from using the new weight (171) in the denominator instead of the original weight—a common mistake that inflates the percentage. Choice D (9.5%) appears to be a distractor with no clear mathematical relationship to the correct calculation. Remember that percent decrease always uses the original value as the denominator, not the final value. A helpful check: the person lost 14 pounds out of 185, which should be less than 10% since 14 is much less than 18.5 (which would be 10% of 185). This confirms that 7.6% makes sense.
A scientist observes a bacterial culture that grows by 25% in the first hour and then decreases by 40% in the second hour. If the final count is 3,000 bacteria, what was the overall percent change from the initial number of bacteria to the final number?
Answer: A 25% decrease First, find the initial number of bacteria. Let the initial number be N. After the first hour, the count is $N \times 1.25$ . After the second hour, the count is $(N \times 1.25) \times (1 - 0.40) = N \times 1.25 \times 0.60 = 0.75N$ . We are given that the final count is 3,000, so $0.75N = 3000$ . Solving for N gives $N = 3000 / 0.75 = 4000$ . The initial number was 4,000. Now, calculate the overall percent change from the initial (4,000) to the final (3,000). The change is $3000 - 4000 = -1000$ . The percent change is $\frac{-1000}{4000} \times 100\% = -0.25 \times 100\% = -25\%$ . This is a 25% decrease. A is incorrect and results from simply subtracting the percentages: 25% - 40% = -15%. C is incorrect because it has the wrong sign. D is incorrect because it uses the final value as the base for the percent change calculation: $(-1000) / 3000 \approx -33.3\%$ .
The population of a small town rose from 12,600 residents to 14,175 residents over five years. What was the percent increase?
Answer: 12.5\% Percent increase questions test your ability to calculate how much a quantity has grown relative to its original value. When you see population changes, price increases, or growth over time, you're looking for the percent change formula. To find percent increase, you need three steps: find the actual increase, divide by the original amount, then convert to a percentage. The population grew from 12,600 to 14,175 residents, so the actual increase is $14,175 - 12,600 = 1,575$ residents. Now divide this increase by the original population: $\frac{1,575}{12,600} = 0.125$ . Converting to a percentage: $0.125 \times 100\% = 12.5\%$ . This confirms answer B is correct. Looking at the wrong answers: A) 11.1% is too low and likely comes from calculation errors or rounding mistakes. C) 13.8% might result from dividing the increase by the new population instead of the original ( $\frac{1,575}{14,175} \approx 0.111$ , but even this doesn't match exactly). D) 15.3% is significantly too high and could come from various computational errors or misreading the numbers. Remember the percent increase formula: $\frac{\text{new value} - \text{original value}}{\text{original value}} \times 100\%$ . Always divide by the original value, not the new one. On the TEAS, double-check that you're using the right starting point for your calculation, as this is where most errors occur in percent change problems.
Use the table to answer the question. What was the percent increase in revenue from Q1 to Q2?
Answer: 17.70% Increase $=96.5-82=14.5.$ Percent increase $=\dfrac{14.5}{82}\times100\approx17.68\%,$ or 17.7\%. A, C, D result from rounding errors, using 96.5 as the base, or arithmetic slips.
The number of employees at a company decreased by 15% from 2020 to 2021. In 2022, the company hired 60 new employees, which brought the total number of employees back to the 2020 level. What was the percent increase in the number of employees from 2021 to 2022, rounded to the nearest tenth of a percent?
Answer: 17.6% Let E be the number of employees in 2020. In 2021, the number was $E \times (1 - 0.15) = 0.85E$ . The decrease in employees was $E - 0.85E = 0.15E$ . In 2022, 60 employees were hired to return to the 2020 level, which means the 60 new hires exactly replaced the number of employees lost. So, $0.15E = 60$ . Solving for E gives $E = 60 / 0.15 = 400$ employees in 2020. The number of employees in 2021 was $400 \times 0.85 = 340$ . The percent increase from 2021 to 2022 is calculated with the 2021 number as the base. The increase was 60 employees. $\frac{60}{340} \times 100\% = \frac{6}{34} \times 100\% \approx 0.17647 \times 100\% \approx 17.6\%$ . A is incorrect because it assumes that to reverse a 15% decrease, a 15% increase is needed, which ignores the change in the base value. B is incorrect and might result from using the average of the 2021 and 2022 employee counts as the base. D is incorrect and could be the result of a calculation error.
A nurse's salary was $60,000 in 2020. In 2021, she received a 5% raise. In 2022, she received a $4,800 raise. What was the percent increase of her salary from 2021 to 2022?
Answer: 7.6% First, calculate the 2021 salary. A 5% raise on $60,000 is $\$60,000 \times 0.05 = \$3,000$ . The 2021 salary was $\$60,000 + \$3,000 = \$63,000$ . Next, calculate the 2022 salary by adding the $4,800 raise to the 2021 salary: $\$63,000 + \$4,800 = \$67,800$ . The question asks for the percent increase from 2021 to 2022. The base for this calculation is the 2021 salary ($63,000), and the change is $4,800. The percent increase is $\frac{\$4,800}{\$63,000} \times 100\% \approx 0.07619 \times 100\% \approx 7.6\%$ . B is incorrect because it uses the original 2020 salary as the base: $\$4,800 / \$60,000 = 8.0\%$ . C is incorrect because it uses the final 2022 salary as the base: $\$4,800 / \$67,800 \approx 7.1\%$ . D is incorrect because it calculates the total percent increase from 2020 to 2022: $(\$7,800 / \$60,000) = 13.0\%$ .

Start this quiz