After learning how to fly, Wendy reduced her daily commute time by $75 \%$ . Previously, her commute took $m$ minutes. $\newline$ Which of the following expressions could represent Wendy's commute time, in minutes, after she learned how to fly? $\newline$ Choose $2$ answers: $\newline$ A $0.25 m$ $\newline$ B $\frac{1}{4} m$ $\newline$ c $1.75 m$ $\newline$ D $0.75 m$ $\newline$ E $\frac{3}{4} m$

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Grade 7

Identify equivalent linear expressions: word problems

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Q. After learning how to fly, Wendy reduced her daily commute time by

75 \%

. Previously, her commute took

m

minutes.

\newline

Which of the following expressions could represent Wendy's commute time, in minutes, after she learned how to fly?

\newline

Choose

2

answers:

\newline

0.25 m

\newline

\frac{1}{4} m

\newline

1.75 m

\newline

0.75 m

\newline

\frac{3}{4} m

Understand the problem: Let's first understand the problem. Wendy reduced her commute time by $75\%$ . This means she now only spends $25\%$ of her original commute time, which was $m$ minutes.
Calculate $25\%$ of $m$ : To find $25\%$ of $m$ , we can multiply $m$ by $0.25$ . This is because $25\%$ as a decimal is $0.25$ . $\newline$ Calculation: $0.25 \times m$
Check given options: Alternatively, we can express $25\%$ as a fraction, which is $\frac{1}{4}$ . So, $\frac{1}{4}$ of $m$ is another way to represent Wendy's new commute time. $\newline$ Calculation: $\left(\frac{1}{4}\right) * m$
Check given options: Alternatively, we can express $25\%$ as a fraction, which is $\frac{1}{4}$ . So, $\frac{1}{4}$ of $m$ is another way to represent Wendy's new commute time. $\newline$ Calculation: $(\frac{1}{4}) \times m$ Now let's check the given options to see which ones match our calculations. $\newline$ Option A is $0.25 m$ , which is correct as we calculated earlier. $\newline$ Option B is $(\frac{1}{4})m$ , which is also correct as it's another way to express $25\%$ of $m$ . $\newline$ Option C is $1.75 m$ , which would mean an increase in her commute time, not a reduction, so this is incorrect. $\newline$ Option D is $\frac{1}{4}$ $0$ , which would represent a $25\%$ reduction, not the $\frac{1}{4}$ $2$ reduction we're looking for, so this is incorrect. $\newline$ Option E is $\frac{1}{4}$ $3$ , which would represent a $25\%$ commute time, not a $\frac{1}{4}$ $2$ reduction, so this is incorrect.