Mrs. Conley asks her class what kind of party they want to have to celebrate their excellent behavior. Out of all the students in the class, $5$ want an ice cream party, $7$ want a movie party, $10$ want a costume party, and the rest are undecided. $\newline$ If $20 \%$ want an ice cream party, how many students are in the class? $\newline$ students

Full solution

Q. Mrs. Conley asks her class what kind of party they want to have to celebrate their excellent behavior. Out of all the students in the class,

5

want an ice cream party,

7

want a movie party,

10

want a costume party, and the rest are undecided.

\newline

20 \%

want an ice cream party, how many students are in the class?

\newline

students

Understand the problem: Understand the problem and what is given. $\newline$ We know that $20\%$ of the students want an ice cream party and that $5$ students have chosen this option.
Convert percentage to decimal: Write $20\%$ as a decimal to use in calculations. $20\% = \frac{20}{100} = 0.20$
Set up equation for total students: Set up the equation to find the total number of students in the class. $\newline$ Let the total number of students be represented by ' $x$ '. $\newline$ According to the problem, $20\%$ of ' $x$ ' is equal to $5$ (since $5$ students want an ice cream party). $\newline$ So, we have $0.20 \times x = 5$
Solve for total students: Solve the equation for ' $x$ ' to find the total number of students. $\newline$ Divide both sides of the equation by $0.20$ to isolate ' $x$ '. $\newline$ $x = \frac{5}{0.20}$ $\newline$ $x = 25$
Verify the solution: Verify the solution. $\newline$ If there are $25$ students in the class, then $20\%$ of $25$ should be equal to $5$ . $\newline$ $0.20 \times 25 = 5$ $\newline$ This is true, so our solution is correct.