Question

part a: identify the change
for each situation, circle whether it is an increase or decrease.

1. the price of a movie ticket goes from $8 to $10.

increase / decrease

1. a sweater originally costs $50 and is on sale for $35.

increase / decrease

1. the number of students in a club goes from 20 to 25.

increase / decrease

1. a video game price drops from $60 to $45.

increase / decrease

part b: calculate percent of change
find the percent of change for each problem.

1. a backpack costs $40 and later costs $50.

original value:
new value:
percent of change

1. a pair of shoes was originally $80 and is now $60.

Explanation:

Part A:

1. Brief Explanations: The price goes from $8 to $10, which is a rise in price. So it's an increase.

Step 1: Determine Original and New Values

Original Value ($O$) = $40$, New Value ($N$) = $50$

Step 2: Calculate the Change in Value

Change ($\Delta$) = $N - O$ = $50 - 40 = 10$

Step 3: Calculate Percent of Change

Percent of Change ($P$) = $\frac{\Delta}{O} \times 100\%$ = $\frac{10}{40} \times 100\% = 25\%$

Step 1: Determine Original and New Values

Original Value ($O$) = $80$, New Value ($N$) = $60$

Step 2: Calculate the Change in Value

Change ($\Delta$) = $O - N$ (since it's a decrease) = $80 - 60 = 20$

Step 3: Calculate Percent of Change

Percent of Change ($P$) = $\frac{\Delta}{O} \times 100\%$ = $\frac{20}{80} \times 100\% = 25\%$ (decrease, but the question asks for percent of change, so the value is $25\%$)

Answer:

**: Increase

1. Brief Explanations: The sweater's price goes from $50 to $35, which is a drop in price. So it's a decrease.