Write an expression for the original number who prefer online resources ($60\%$ of $N$), and another expression for the new number after 12 more students choose online resources.

The problem says that after adding 12 students, the percentage becomes $65\%$. How can you set the new number of online-resource students equal to $65\%$ of the total, in equation form?

Once you have an equation like $0.60N + 12 = 0.65N$, isolate $N$ step by step. Be careful when subtracting and when dividing by a decimal.

In Desmos, type y = 0.60x + 12 on one line and y = 0.65x on another line. This represents each side of the equation $0.60x + 12 = 0.65x$ as a separate graph.

Look for the point where the two lines intersect. Tap or click on that intersection. The x-coordinate of this point is the value of the total number of students that satisfies the equation.

Let $N$ be the total number of students surveyed.

• $60\%$ of the students prefer online resources, so the number of students who originally preferred online resources is $0.60N$.

If 12 more students had chosen online resources, the number preferring online resources would be $0.60N + 12$.

According to the problem, in that case $65\%$ of the students would prefer online resources. That is $0.65N$ students.

So we can write the equation:

Now solve this equation for $N$ step by step (but do not compute the final value yet). Move the $0.60N$ term to the right side:

From the last equation we have

To solve for $N$, divide both sides by $0.05$:

Compute this value:

• $0.05 = \frac{5}{100} = \frac{1}{20}$, so dividing by $0.05$ is the same as multiplying by 20.
• $12 \times 20 = 240$.

Therefore, the total number of students surveyed is 240.