Math Problem Statement

Skylar needs to buy a pair of dress pants for $40, a shirt for $30, and a tie for $20.

Skylar has three coupons.

The first coupon gives him x percent off on a shirt.

The second coupon gives him y percent off on the dress pants.

The third coupon gives him z percent off on his total purchase. 

He cannot combine the coupon for the total purchase with the other two coupons. These expressions give both possibilities for the total cost of Skylar's purchase after the coupons are applied. The variables represent percentages as decimals.

(1−x)30+(1−y)40+20

(1−z)(40+30+20)   Skylar uses the dress pants coupon.

Which part of the expression represents the percent that Skylar will pay for the dress pants?   Responses

40 + 30 + 20

40 + 30 + 20

(1−y)

1 minus y

40(1−y)

40 left parenthesis 1 minus y right parenthesis

40

Solution

The part of the expression that represents the percent that Skylar will pay for the dress pants is:

40(1−y)

This expression shows that Skylar will pay 1y1-y (the percentage he has to pay after the discount) multiplied by the original price of the dress pants, which is $40.

If you have any more questions or need further explanation, feel free to ask!

Here are five related questions:

  1. What does the expression (1x)30(1−x)30 represent in the context of this problem?
  2. If Skylar has a 25% discount on the dress pants, what is the new cost of the pants?
  3. How would the expression change if Skylar used the total purchase coupon instead?
  4. What does the term 2020 represent in the first expression?
  5. How would you calculate the total cost if Skylar used both the dress pants and the shirt coupons?

Tip: When working with percentages in expressions, remember that a percentage off is represented by (1percentage as a decimal)(1 - \text{percentage as a decimal}).

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Math Problem Analysis

Mathematical Concepts

Percentages
Discounts
Arithmetic Operations

Formulas

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Theorems

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Suitable Grade Level

High School