Question

Terrance used this expression to find the final price, in dollars, of a hat that is discounted 30% off the original price of $20.

20−(20×0.3)

Which of the following is an equivalent expression?

Answer 1

To find an equivalent expression to Terrance's expression \( 20 - (20 \times 0.3) \), we can simplify it.

First, let's break down the original expression:

1. Calculate \( 20 \times 0.3 = 6 \).
2. Substitute that back into the expression:\( 20 - 6 \).
3. This simplifies to \( 14 \).

Now, let's find an equivalent expression that results in the same final price. Since the hat is discounted 30%, we can also express this in terms of finding just the price after the discount directly.

The equivalent expression can also be calculated using the original price and the discount rate like this:

**Final Price = Original Price × (1 - Discount Rate)**

The original price is \( 20 \) and the discount rate is \( 0.3\).

So:

**Final Price = \( 20 \times (1 - 0.3) \)**
**Final Price = \( 20 \times 0.7 \)**

Calculating \( 20 \times 0.7 = 14 \).

Thus, an equivalent expression to Terrance's original expression is:

**\( 20 \times 0.7 \)** or alternatively \( 20 \times (1 - 0.3) \).

Both expressions will yield the same final price of \( 14 \) dollars.