Question

the drama department at millersburg high school had 24 students try out for the musical this spring, which is 20% fewer than tried out last spring. how many students auditioned last spring? students

Explanation:

Step1: Find the percentage of students this spring

This spring, the number of students is 20% fewer than last spring. So the percentage of students this spring is \(100\% - 20\% = 80\%\) or \(0.8\) in decimal.

Step2: Calculate the number of students this spring

Last spring, there were 24 students. To find the number of students this spring, we multiply the number of students last spring by the percentage (in decimal) of students this spring. So we calculate \(24\times0.8\).
\(24\times0.8 = 19.2\)? Wait, no, maybe I misread. Wait, the problem is: The drama department had 24 students try out for the musical this spring, which is 20% fewer than tried out last spring. Wait, no, wait the text: "The drama department at Millersburg High School had 24 students try out for the musical this spring, which is 20% fewer than tried out last spring. How many students auditioned last spring?" Wait, maybe I misread the direction. Wait, let's re - read.

Wait, the correct interpretation: Let \(x\) be the number of students who auditioned last spring. This spring, the number is 20% fewer than last spring, so this spring's number is \(x-0.2x = 0.8x\). And this spring's number is 24. So we have the equation \(0.8x=24\).

Step1: Set up the equation

Let \(x\) be the number of students last spring. The number of students this spring is 20% less than last spring, so the number of students this spring is \(x(1 - 0.2)=0.8x\). We know this spring's number is 24, so \(0.8x = 24\).

Step2: Solve for \(x\)

To solve for \(x\), we divide both sides of the equation \(0.8x = 24\) by \(0.8\). So \(x=\frac{24}{0.8}\).
\(\frac{24}{0.8}=\frac{240}{8}=30\).

Wait, maybe the original problem was mis - presented. Wait, the user's image: "The drama department at Millersburg High School had 24 students try out for the musical this spring, which is 20% fewer than tried out last spring. How many students auditioned last spring?"

So the correct steps:

Step1: Define the variable

Let \(x\) = number of students who auditioned last spring.

Step2: Write the relationship

This spring's number is 20% less than last spring's, so this spring's number = last spring's number - 20% of last spring's number. Mathematically, \(24=x - 0.2x\) or \(24 = 0.8x\).

Step3: Solve for \(x\)

Divide both sides by 0.8: \(x=\frac{24}{0.8}=30\).

But if the problem was "How many students auditioned this spring, given that last spring was \(x\) and this spring is 20% less", but from the text in the image: "The drama department at Millersburg High School had 24 students try out for the musical this spring, which is 20% fewer than tried out last spring. How many students auditioned last spring?"

Wait, maybe I made a mistake in the initial reading. Let's assume the problem is: This spring, 24 students tried out, which is 20% less than last spring. Find last spring's number.

So the formula: Let \(L\) be last spring's number. Then \(24 = L\times(1 - 0.2)\), so \(L=\frac{24}{0.8}=30\).

But if the problem was "How many students auditioned this spring, given that last spring was, say, 30, and this spring is 20% less", then \(30\times0.8 = 24\). But the question in the image is "How many students auditioned last spring?"

So the correct answer is 30.

Answer:

30