Finding Percent Change

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Basic Math › Finding Percent Change

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is decreased to . What is the percent change?

Explanation

Percent change is found by the following formula:

$\text{Percent Change}=\frac{\text{Amount Change}}{\text{Original Amount}}\times 100$

Amount change is the difference between the old amount and the new amount.

Here, the original amount is 30, and the new amount is 27. The difference between them is:

We plug in 3 for amount change and 30 for original amount and simplify:

$\text{Percent Change}=\frac{3}{30}\times 100$

$\text{Percent Change}=\frac{3}{30}\times100=.1\times 100=10$

Our final answer is 10%.

In March, an athlete weighed pounds. In April, the same athlete weighed pounds. What is the athlete's percentage of weight loss?

Explanation

The formula to find percentage change is

$\bigg(\frac{new-original}{original}\bigg)\times100$ .

So for our athlete, our new weight is 170 pounds, and the original weight is 195 pounds.

$\bigg(\frac{170-195}{195}\bigg)\times100=\bigg(\frac{-25}{195}\bigg)\times100=-12.8%$

Because the question already tells us that we need to find the percent lost, or percent decrease, we can drop the negative sign in the answer.

In March, an athlete weighed pounds. In April, the same athlete weighed pounds. What is the athlete's percentage of weight loss?

Explanation

The formula to find percentage change is

$\bigg(\frac{new-original}{original}\bigg)\times100$ .

So for our athlete, our new weight is 170 pounds, and the original weight is 195 pounds.

$\bigg(\frac{170-195}{195}\bigg)\times100=\bigg(\frac{-25}{195}\bigg)\times100=-12.8%$

Because the question already tells us that we need to find the percent lost, or percent decrease, we can drop the negative sign in the answer.

is decreased by . What is the new number?

Explanation

We first find 18% of 76:

$76\times .18=13.68$

Since 76 is being decreased by this amount, we subtract 13.68:

is decreased to . What is the percent change?

Explanation

Percent change is found by the following formula:

$\text{Percent Change}=\frac{\text{Amount Change}}{\text{Original Amount}}\times 100$

Amount change is the difference between the old amount and the new amount.

Here, the original amount is 30, and the new amount is 27. The difference between them is:

We plug in 3 for amount change and 30 for original amount and simplify:

$\text{Percent Change}=\frac{3}{30}\times 100$

$\text{Percent Change}=\frac{3}{30}\times100=.1\times 100=10$

Our final answer is 10%.

is decreased by . What is the new number?

Explanation

We first find 18% of 76:

$76\times .18=13.68$

Since 76 is being decreased by this amount, we subtract 13.68:

At age you are inches taller than you were years ago, when you were inches tall. What is the percent change in your height from years ago to now? Round your answer to the nearest tenth.

Explanation

The questions throws a lot of numbers at us, but the only ones we are concerned with are those having to do with height. We use the following formula:

$\text{Percent Change}=\frac{\text{Amount Change}}{\text{Original Amount}}\times 100$

We want to know the percent change. We know the amount change, 6 inches, and the original amount, 52 inches. Plugging these into the formula, we get:

$\text{Percent Change}=\frac{6}{52}\times 100=11.538462$

Rounding this number to the nearest tenth gives us 11.5%.

Derek ran his first mile in minutes and his second mile in minutes.

What is the percent increase between the time it took Derek to run the first and second mile?

Explanation

The correct answer is a percent change (increase) of .

This can be calculated using the following equation:

$\frac{\text{new}-\text{original}}{\text{original}}\cdot100 = \frac{11-10}{10}\cdot100 = \frac{1}{10} \cdot 100 = 10$

Therefore, the answer is a percent increase of .

In May of the past year, Harry's company made in profit, and in June of that same year, his company made in profit. By what percent did his profit increase from May to June?