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) $0.75 h$ $\newline$ (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

(A)

h(1-0.75)

\newline

(B)

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

\newline

(C)

\frac{3}{4}h

\newline

(D)

0.75 h

\newline

(E)

\frac{1}{4}h

Understand $75$ % Calculation: First, we need to understand that $75\%$ of the original length means we are looking for an expression that multiplies the original length $h$ by $0.75$ or by the fraction equivalent of $75\%$ , which is $\frac{75}{100}$ or $\frac{3}{4}$ .
Evaluate Option A: Now let's evaluate each option: $\newline$ A. $h(1-0.75)$ simplifies to $h(0.25)$ or $\frac{h}{4}$ , which represents $25\%$ of the original length, not $75\%$ .
Evaluate Option B: B. $(1-(\frac{75}{100}))h$ simplifies to $(1-0.75)h$ which is the same as $h(0.25)$ or $\frac{h}{4}$ , again representing $25\%$ of the original length, not $75\%$ .
Evaluate Option C: C. $\frac{3}{4}h$ is the same as $0.75h$ , which correctly represents $75\%$ of the original length.
Evaluate Option D: D. $0.75h$ directly represents $75\%$ of the original length, which is correct.
Evaluate Option E: E. $(1)/(4)h$ is the same as $h/4$ or $h(0.25)$ , which represents $25\%$ of the original length, not $75\%$ .