Question

chad bought a watch that normally costs w dollars. he used a 30% discount.
the expression 0.7w describes the amount of money chad paid for the watch. we can also use the expression w - 0.3w to represent the same quantity.
match each amount in the situation with the expression that represents it.

situation	expression
amount of the discount	0.3w
percent decrease of the discount, as a decimal	w

Explanation:

Step1: Analyze "Amount the watch normally costs"

The problem states the watch normally costs \( w \) dollars, so this matches the expression \( w \).

Step2: Analyze "Amount of the discount"

A 30% discount on \( w \) dollars means \( 0.3 \times w = 0.3w \), so this matches \( 0.3w \).

Step3: Analyze "Percent decrease of the discount, as a decimal"

A 30% discount means the percent decrease as a decimal is \( 0.3 \)? Wait, no—wait, the amount paid is \( 0.7w \), which is \( 1 - 0.3 = 0.7 \) of the original price. So the percent decrease (the decimal representing the discount rate) is \( 0.3 \)? Wait, no, the question says "Percent decrease of the discount, as a decimal"—wait, maybe it's the decimal for the remaining percentage. Wait, the discount is 30% or 0.3, so the percent decrease (the decimal for the discount rate) is 0.3? But the expression given is 0.7. Wait, no—wait, the amount paid is 70% of the original, which is 0.7 as a decimal. So "Percent decrease of the discount, as a decimal"—wait, maybe it's the decimal for the fraction of the original price paid. So 70% is 0.7, so that matches 0.7.

Wait, let's re-express:

• Normal cost: \( w \) (given as "normally costs \( w \) dollars")
• Discount amount: 30% of \( w \), which is \( 0.3w \)
• Percent decrease (the decimal for the fraction paid, since after 30% discount, you pay 70%, which is 0.7 as a decimal)

So:

• Amount the watch normally costs: \( w \)
• Amount of the discount: \( 0.3w \)
• Percent decrease of the discount, as a decimal: \( 0.7 \) (since 1 - 0.3 = 0.7, representing 70% of the original price paid, which is the percent remaining, but the "percent decrease" in terms of the decimal for the discount's effect—maybe the decimal for the fraction of the price paid, which is 0.7)

Answer:

• Amount the watch normally costs: \( w \)
• Amount of the discount: \( 0.3w \)
• Percent decrease of the discount, as a decimal: \( 0.7 \)