We are asked to find how many students are remaining in the cafeteria. Let's start by visualizing the situation given in the exercise. At the beginning, there were 100 students in a middle school cafeteria. We are given that 70 % of the students in the cafeteria bought their lunch.
We can find the number of students that bought their lunch by multiplying 70 % by 100. Remember that we can write the percent as a fraction by writing the number part as a numerator over 100.
This means that 70 students in the cafeteria bought their lunch.
We know that some of the students that bought their lunch left the cafeteria to attend an assembly.
Let x be the number of students that left the cafeteria.
Now, the students that bought their lunch make up 60 % of the remaining students. We can use this information to write a percent proportion that will help us to find the value of x. A percent proportion is a proportion that sets the ratio of a part of a whole equal to the ratio of a percent out of 100.
part/whole=percent/100
Let's take a look at our diagram to identify the part and whole for the given situation.
We can write this as a percent proportion.
70-x/100-x=60/100
Now we can solve the proportion that we got for x. Remember, the cross products of any proportion are equal. We will also use the Distributive Property and the Properties of Equality to help us.
We got that x=25 is the solution to the proportion. Since the expression (100-x) represents the number of students that are remaining in the cafeteria, we can substitute x=25 into this term and simplify to find the number of students remaining in the cafeteria. Let's do it!
100-x = 100-25=75
We found that there are 75 students still in the cafeteria.
