According to a website where users review their doctors, $116$ out of $119$ users would recommend Dr. Gutierrez to their friends and family. If the website users are representative of Dr. Gutierrez's $1$ , $293$ patients, about how many patients would recommend Dr. Gutierrez to their friends and family? $\newline$ (Round your answer to the nearest whole number.)

Full solution

Q. According to a website where users review their doctors,

116

out of

119

users would recommend Dr. Gutierrez to their friends and family. If the website users are representative of Dr. Gutierrez's

1

293

patients, about how many patients would recommend Dr. Gutierrez to their friends and family?

\newline

(Round your answer to the nearest whole number.)

Identify given information: Identify the given information and what we need to find. $\newline$ We have: $\newline$ Number of users who would recommend Dr. Gutierrez: $116$ $\newline$ Total number of users who reviewed: $119$ $\newline$ Total number of Dr. Gutierrez's patients: $1,293$ $\newline$ We need to estimate how many of Dr. Gutierrez's patients would recommend him.
Set up proportion: Set up a proportion to represent the relationship between the number of users who recommend the doctor and the total number of users, and apply this proportion to the total patient count. $\newline$ $\frac{\text{users who recommend}}{\text{total users}} = \frac{\text{patients who would recommend}}{\text{total patients}}$ $\newline$ $\frac{116}{119} = \frac{x}{1,293}$
Solve for x: Solve for x, which represents the estimated number of patients who would recommend Dr. Gutierrez. $\newline$ Cross multiply to solve for x. $\newline$ $116 \times 1,293 = 119 \times x$
Perform multiplication: Perform the multiplication on both sides of the equation. $\newline$ $116 \times 1,293 = 150,188$ $\newline$ $119 \times x = 150,188$
Divide to solve for x: Divide both sides of the equation by $119$ to solve for $x$ . $\newline$ $x = \frac{150,188}{119}$ $\newline$ $x \approx 1,262.08$
Round the answer: Round the answer to the nearest whole number, as the question asks for an estimate. $x \approx 1,262$