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The expression
1.16(0.75 p) represents the amount Aubrey 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?

116% tip and then a discount of
75%

0.16% tip and then a discount of
75%
A discount of
75% and then
16% tip
A discount of
25% and then
16% tip

The expression $1.16(0.75 p)$ represents the amount Aubrey 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? $\newline$ $116 \%$ tip and then a discount of $75 \%$ $\newline$ $0.16 \%$ tip and then a discount of $75 \%$ $\newline$ A discount of $75 \%$ and then $16 \%$ tip $\newline$ A discount of $25 \%$ and then $16 \%$ tip

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Interpret regression lines

Full solution

Q. The expression

1.16(0.75 p)

represents the amount Aubrey 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

116 \%

tip and then a discount of

75 \%

\newline

0.16 \%

tip and then a discount of

75 \%

\newline

A discount of

75 \%

and then

16 \%

tip

\newline

A discount of

25 \%

and then

16 \%

tip

Understand the expression: Understand the expression $1.16(0.75p)$ . This expression represents two consecutive changes to the original price $p$ . The first change is represented by $0.75p$ , which suggests a reduction to $75\%$ of the original price, indicating a $25\%$ discount. The second change is represented by multiplying the discounted price by $1.16$ , which suggests adding a $16\%$ tip to the discounted price.
Analyze first option: Analyze the first option, ＂ $116$ % tip and then a discount of $75$ %.＂ This would mean applying a $116\%$ tip on the original price and then reducing the resulting amount by $75\%$ . The expression for this would be $(1 + 1.16)p \times 0.75$ , which simplifies to $2.16p \times 0.75$ . This is not the same as the given expression $1.16(0.75p)$ .
Analyze second option: Analyze the second option, ＂ $0.16\%$ tip and then a discount of $75\%$ .＂ This would mean applying a $0.16\%$ tip on the original price and then reducing the resulting amount by $75\%$ . The expression for this would be $(1 + 0.0016)p \times 0.75$ , which simplifies to $1.0016p \times 0.75$ . This is not the same as the given expression $1.16(0.75p)$ .
Analyze third option: Analyze the third option, ＂A discount of $75$ % and then $16$ % tip.＂ This would mean reducing the original price by $75\%$ and then adding a $16\%$ tip to the discounted price. The expression for this would be $0.75p \times 1.16$ , which simplifies to $1.16(0.75p)$ . This matches the given expression.
Analyze fourth option: Analyze the fourth option, ＂A discount of $25\%$ and then $16\%$ tip.＂ This would mean reducing the original price by $25\%$ (making it $75\%$ of the original price) and then adding a $16\%$ tip to the discounted price. The expression for this would be $0.75p \times 1.16$ , which simplifies to $1.16(0.75p)$ . This also matches the given expression.

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