Question

problem 13: spiral review
bettie’s boutique is having a 20% off sale.
select all the equations that represent the relationship between the original price, x, and the sale price, y.
\\( y = 0.8x \\)
\\( y = x - 0.2 \\)
\\( y = x - 0.2x \\)
\\( y = 0.2x \\)
\\( y = (1 - 0.2)x \\)

Explanation:

Step1: Understand the discount logic

A 20% off sale means the sale price $y$ is 80% of the original price $x$, since $100\% - 20\% = 80\% = 0.8$. This gives the equation $y=0.8x$.

Step2: Simplify equivalent expressions

We can rewrite 0.8 as $1-0.2$, so substituting this into the equation gives $y=(1-0.2)x$.

Step3: Verify other options

• $y=x-0.2$ subtracts a fixed 0.2, not 20% of $x$, so it is incorrect.
• $y=x-0.2x$ simplifies to $y=0.8x$, which is equivalent to the correct relationship.
• $y=0.2x$ represents the discount amount, not the sale price, so it is incorrect.

Answer:

• $y=0.8x$
• $y=x-0.2x$
• $y=(1-0.2)x$