Taking successive discounts of 15% off and then 25% off is the same as taking a one time discount of 40%.

Question

Please select the best answer from the choices provided

T
F

Answer 1

The statement is False.

To see why, let's calculate the combined effect of the two successive discounts.

1. Start with an original price of \( P \).
2. After a 15% discount, the price becomes \( P - 0.15P = 0.85P \).
3. Then, applying a 25% discount on the new price: \[ 0.85P - 0.25(0.85P) = 0.85P \times 0.75 = 0.6375P \]

Now, let's compare this to a one-time discount of 40%:

• A 40% discount on the original price is: \[ P - 0.40P = 0.60P \]

Now we see:

• Successive discounts yield \( 0.6375P \)
• A single discount yields \( 0.60P \)

Since \( 0.6375P \) is greater than \( 0.60P \), the two discounts are not equivalent. Thus, the statement is indeed False.