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. If $20 \%$ want an ice cream party, how many students are in the class?

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. If

20 \%

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

Understand Percentage Relationship: Understand the relationship between percentages and actual numbers. $\newline$ We know that $20\%$ of the students want an ice cream party and that $5$ students have chosen this option. To find the total number of students, we need to calculate the whole from the part and the percentage.
Convert Percentage to Decimal: Write $20\%$ as a decimal. $\newline$ $20\% = \frac{20}{100} = 0.20$
Set Up Equation for Total: Set up the equation to find the total number of students. Let the total number of students be represented by ' $x$ '. According to the problem, $20\%$ of ' $x$ ' is equal to $5$ (since $5$ students want an ice cream party). So, we have $0.20 \times x = 5$
Solve for Total: Solve for ' $x$ ' to find the total number of students. $\newline$ Divide both sides of the equation by $0.20$ to isolate ' $x$ '. $\newline$ $x = \frac{5}{0.20}$ $\newline$ $x = 25$