 ## How to Solve Word Problems: Percent of Change

Solving word problems that involve the percent of change can seem daunting initially. However, with a step-by-step approach, they become quite manageable. Here's how to tackle them:

### Step 1: Understand the Concept of Percent of Change

Percent of change is used to describe the relative growth or reduction of an amount. It's the ratio of the change in quantity to the original quantity, expressed as a percentage. The basic formula to calculate the percent of change is:

$$\text{Percent of change} = \frac{{\text{New amount} - \text{Original amount}}}{\text{Original amount}} \times 100\%$$

### Step 2: Identify the Known and Unknown Variables

Before you can solve the problem, identify what you know and what you need to find out. Word problems usually provide the original amount and the new amount, and you're tasked to find the percent of change.

### Step 3: Set Up the Equation

Using the percent of change formula, substitute the values you know from the problem into the equation.

### Step 4: Solve for the Unknown

At this stage, simplify your equation to find the value of the unknown (the percent of change).

### Step 5: Interpret the Solution

If the percent of change is positive, it means an increase; if it's negative, it means a decrease. Remember to include this interpretation as part of your answer.

Always substitute your solution back into the original problem to ensure it's correct.

### Example

Let's say the price of a TV was originally $500 and it increased to$650. What is the percent of change?

1. Identify the known and unknown variables. Original amount is $$\500$$ and new amount is $$\650$$.
2. Set up the equation: $$\text{Percent of change} = \frac{{650 - 500}}{500} \times 100\%$$.
3. Solve for the unknown: $$\text{Percent of change} = \frac{150}{500} \times 100\% = 30\%$$.
4. Interpret the solution: There is a 30% increase in the price of the TV.

Remember, practice is key when it comes to solving word problems. The more problems you solve, the better you'll understand the process.

### Exercises

1) The population of a town increased from 45,000 to 54,000. What was the percent of increase?

2) A computer game cost $70 last year. This year, the price dropped to$49. What is the percent decrease?

3) John's monthly salary increased from $2500 to$2750. Calculate the percent increase.

4) A pair of shoes was originally priced at $85. During a sale, its price dropped to$68. What is the percent decrease?

5) The number of students in a class decreased from 36 to 32. What is the percent decrease?

6) A store sold 120 items one month and 144 items the next month. What is the percent increase in sales?

7) Last year, a company made a profit of $2,500,000. This year, the profit was$2,200,000. What was the percent decrease in profit?

8) The price of a house increased from $250,000 to$300,000. What is the percent increase?

9) The number of cars in a parking lot decreased from 500 to 450. What is the percent decrease?

10) A bag of flour weighed 2 kilograms last month. This month, it weighs 1.8 kilograms. What is the percent decrease in weight?

1)$\frac{{(54000 - 45000)}}{{45000}} \times 100 = 20\%$

2)$\frac{{(70 - 49)}}{{70}} \times 100 = 30\%$

3)$\frac{{(2750 - 2500)}}{{2500}} \times 100 = 10\%$

4)$\frac{{(85 - 68)}}{{85}} \times 100 = 20\%$

5)$\frac{{(36 - 32)}}{{36}} \times 100 = 11.11\%$

6)$\frac{{(144 - 120)}}{{120}} \times 100 = 20\%$

7)$\frac{{(2500000 - 2200000)}}{{2500000}} \times 100 = 12\%$

8)$\frac{{(300000 - 250000)}}{{250000}} \times 100 = 20\%$

9)$\frac{{(500 - 450)}}{{500}} \times 100 = 10\%$

10)$\frac{{(2 - 1.8)}}{{2}} \times 100 = 10\%$

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