Question

1. during his move to a new house, raj lost 24% of his dvd collection. if raj had 225 dvds before the move, how many dvds did he lose?

increase or decrease? _______________
amount of change = _______________
original amount = _______________
percent = _______________
substitute and solve:

final result:

Explanation:

Step1: Determine increase/decrease

Since Raj lost DVDs, the number of DVDs decreased. So it's a decrease.

Step2: Identify amount of change (unknown)

Let the amount of change (number of DVDs lost) be \( x \). We need to find \( x \).

Step3: Identify original amount

The original amount of DVDs is 225.

Step4: Identify percent

The percent of change is 24% or 0.24 in decimal.

Step5: Substitute and solve

The formula for percent change is \( \text{percent} = \frac{\text{amount of change}}{\text{original amount}} \). Substituting the known values: \( 0.24=\frac{x}{225} \). To solve for \( x \), multiply both sides by 225: \( x = 225\times0.24 \). Calculating \( 225\times0.24 \): \( 225\times0.2 = 45 \), \( 225\times0.04 = 9 \), so \( 45 + 9 = 54 \).

Answer:

Increase or decrease? decrease
amount of change = 54
original amount = 225
percent = 24%
Substitute and solve: \( x = 225\times0.24 = 54 \)
Final result: 54