Algebra - How to find the percent of increase

Find the percent of increase from $\small 15$ to $\small 24$ .

$\small 60%$

$\small 40%$

$\small 90%$

$\small 15%$

Explanation

For this type of problem we use this formula:

$\small \frac{difference}{original} \times 100$ .

"Difference" is simply the difference between the two numbers given, and "original" is the number that is stated usually after the word "from" , example: from $\small #$ ____ to ____.

In this problem our formula will be filled in as follows:

$\small \small \frac{24-15}{15} \times 100 = \frac{9}{15}\times 100 = 60%$ .

This is our percent increase.

There are 3000 people enrolled in a specific program in 2003. Between 2003 and 2004, the number of people enrolled increases by 12%, and between 2004 and 2005, 65 people unenroll. How many people are enrolled at the beginning of 2005?

Explanation

Between 2003 and 2004, the number of people enrolled increases by 12%:

$3000\cdot 1.12=3360$

Between 2004 and 2005, 65 people unenroll:

Last week, a gallon of milk cost $3.00. This week, the cost of a gallon of milk is $3.75. Find the percent increase.

Explanation

To find the percent increase, we use the following formula:

$\text{percent increase} = \frac{\text{new price - original price}}{\text{original price}} \cdot 100$

$\text{percent increase} = \frac{$3.75 - $3.00}{$3.00} \cdot 100$

$\text{percent increase} = \frac{$0.75}{$3.00} \cdot 100$

$\text{percent increase} = 0.25 \cdot 100$

$\text{percent increase} = 25%$

Sally currently makes $90000 per year as an engineer. After several years working for her engineering firm, Sally's supervisor notices superior quality of Sally's work, and decides to raise her annual salary to $112500. By what percentage did Sally's salary increase?

Explanation

The general formula for calculating percent change is $\frac{new-original}{original}*100$

In our case, the new (value) is Sally's new salary and the original (value) is her old salary. Plug these values into our equation and simplify.

$\frac{112,500-90,000}{90,000}*100$

Last month you got paid $10 an hour at your job. You went under review this month, and they said they are increasing your pay to $12 an hour. Find the percent increase.

Explanation

To find percent increase, we use the formula

$\text{percent increase} = \frac{\text{new amount - original amount}}{\text{original amount}} \cdot 100$

We can substitute into the formula. We get

$\text{percent increase} = \frac{$12 - $10}{$10} \cdot 100$

$\text{percent increase} = \frac{$2}{$10} \cdot 100$

$\text{percent increase} = 20$

Therefore, the percent increase is equal to 20%.

A garbage collector is able to finish his daily route in 5 hours. The city decides to give him a larger route. Now his route takes 8 hours to complete. What is the percentage change in the amount of time his route takes him to complete?

Explanation

This is a simple percentage change problem. Use the formula new amount subtracted by old amount then divided by old amount and multiplied by 100.

$\frac{8-5}{5}\cdot 100$

$\frac{3}{5}\cdot 100$

$0.6\cdot 100$

The amount of time the route takes the garbage collector increased by 60%

If the number of Republican voters in a certain district has decreased from 150,000 to 78,560, what is the percent decrease in the number of Republican voters?

Explanation

If the number of Republican voters in a certain district has decreased from 150,000 to 78,560, what is the percent decrease in the number of Republican voters?

To find the percent of decrease, we need to divide the difference by the original number:

$\frac{71440}{150000}=.476\approx48%$

So the number of Republican voters decreased by about

Find the percent increase from to .

$\approx 5.7%$

$\approx 4.7%$

$\approx 5.9%$

$\approx 2.7%$

Explanation

For this type of problem we use this formula:

$\frac{difference}{original} \times 100$

"Difference" is simply the difference between the two numbers given, and "original" is the number that is stated usually after the word "from" , example: from ____ to ____. In this problem our formula will be filled in as follows:

$\frac{37-35}{35}\times 100 = \frac {2}{35}\times 100 \approx 5.7%$

This our percent increase.

Find the percent increase from to .

Explanation

For this type of problem we use this formula: $\frac{difference}{original} \times 100$ . "Difference" is simply the difference between the two numbers given, and "original" is the number that is stated usually after the word "from" , example: from ____ to ____. In this problem our formula will be filled in as follows: $\frac{23-20}{20}\times 100 = \frac {3}{20}\times 100 = 15%$ . This is our percent increase.