On Monday, Florencia's hair was $h$ centimeters long. She got a haircut on Tuesday, so her hair was only $75\%$ of the length it was on Monday. $\newline$ Which of the following expressions could represent how many centimeters long Florencia's hair was after the haircut? $\newline$ Choose $2$ answers: $\newline$ A $h(1-0.75)$ $\newline$ B $(1-(\frac{75}{100}))h$ $\newline$ C $(\frac{3}{4})h$ $\newline$ D $0.75h$ $\newline$ E $(\frac{1}{4})h$

Full solution

Q. On Monday, Florencia's hair was

h

centimeters long. She got a haircut on Tuesday, so her hair was only

75\%

of the length it was on Monday.

\newline

Which of the following expressions could represent how many centimeters long Florencia's hair was after the haircut?

\newline

Choose

2

answers:

\newline

h(1-0.75)

\newline

(1-(\frac{75}{100}))h

\newline

(\frac{3}{4})h

\newline

0.75h

\newline

(\frac{1}{4})h

Understand $75$ % of Length: First, we need to understand that $75\%$ of the original length means Florencia's hair is now three-quarters of what it was on Monday. To find $75\%$ of a number, you can multiply the number by $0.75$ or by the fraction $\frac{3}{4}$ . Let's check each option to see which ones correctly represent $75\%$ of $h$ .
Check Option A: Option A is $h(1-0.75)$ . This means we are taking the full length $h$ and subtracting $75\%$ of $h$ from it. This would give us $25\%$ of $h$ , not $75\%$ .
Check Option B: Option B is $(1-(\frac{75}{100}))h$ . This simplifies to $(1-0.75)h$ , which is the same as option A and would also give us $25\%$ of $h$ , not $75\%$ .
Check Option C: Option C is $(\frac{3}{4})h$ . This means we are taking three-quarters of the original length $h$ , which correctly represents $75\%$ of $h$ .
Check Option D: Option D is $0.75h$ . This means we are taking $75\%$ of the original length $h$ , which is the same as multiplying $h$ by $0.75$ , and this correctly represents $75\%$ of $h$ .
Check Option E: Option E is $(\frac{1}{4})h$ . This means we are taking one-quarter of the original length $h$ , which would represent $25\%$ of $h$ , not $75\%$ .