The expression $1.13(0.55 p)$ represents the amount Chee paid for dinner at a restaurant after she applied a discount coupon and added tip. Which changes to the original price could have resulted in the expression? $\newline$ $0.13 \%$ tip and then a discount of $0.45 \%$ $\newline$ A discount of $0.45 \%$ and then $13 \%$ tip $\newline$ $13 \%$ tip and then a discount of $45 \%$ $\newline$ A discount of $55 \%$ and then $13 \%$ tip

View step-by-step help

Home

Math Problems

Algebra 1

Interpret parts of quadratic expressions: word problems

Full solution

Q. The expression

1.13(0.55 p)

represents the amount Chee paid for dinner at a restaurant after she applied a discount coupon and added tip. Which changes to the original price could have resulted in the expression?

\newline

0.13 \%

tip and then a discount of

0.45 \%

\newline

A discount of

0.45 \%

and then

13 \%

tip

\newline

13 \%

tip and then a discount of

45 \%

\newline

A discount of

55 \%

and then

13 \%

tip

Analyze Expression: Let's analyze the expression $1.13(0.55p)$ to understand what it represents. The expression can be broken down into two parts: $0.55p$ and $1.13$ . The $0.55p$ part represents the price after applying a discount, and the $1.13$ represents the final amount after adding a tip to the discounted price.
Calculate Discount Percentage: To determine the percentage discount, we look at the factor multiplied by $p$ , which is $0.55$ . This means that the original price $p$ is being multiplied by $0.55$ , indicating a $55\%$ of the original price is kept, or equivalently, a $45\%$ discount is applied ( $100\% - 55\% = 45\%$ ).
Apply Tip Percentage: Next, we consider the factor $1.13$ . This factor is applied to the discounted price, which means a $13\%$ tip is added to the price after the discount. To add a $13\%$ tip, you multiply the discounted price by $1 + \frac{13}{100}$ , which equals $1.13$ .
Consider Order of Operations: Now, let's consider the order of operations. Since the tip percentage ( $1.13$ ) is applied to the result of the discounted price ( $0.55p$ ), this means the discount is applied first, followed by the tip.
Sequence of Operations: Therefore, the correct sequence that resulted in the expression $1.13(0.55p)$ is: a discount of $55\%$ was applied to the original price, and then a $13\%$ tip was added to the discounted price.