"20% more questions correctly" refers to the number of correct answers, not the percentage. How do you represent a $20\%$ increase of the quantity $0.75x$?

The second exam has $20$ more questions than the first, so it has $x+20$ questions. If she gets $80\%$ of these correct, what expression gives the number she got right on the second exam?

You now have two expressions for the number correct on the second exam: one from the 20% increase and one from the 80% of $(x+20)$. Set them equal and solve for $x$.

In Desmos, type y = 0.9x on one line and y = 0.8(x + 20) on another line. These represent the two ways of calculating the number of correct answers on the second exam.

Zoom or adjust the viewing window until you see where the two lines intersect. Tap or click the intersection point and read off its $x$-coordinate; that $x$-value is the number of questions on the first exam.

Let $x$ be the number of questions on the first practice exam.

On the first exam, she answered $75\%$ of the questions correctly, so the number of correct answers on the first exam is

First description: She answered 20% more questions correctly than on the first exam.

• $20\%$ more than $0.75x$ means multiply by $1.2$:

So, by this description, she got $0.9x$ questions correct on the second exam.

Second description: The second exam had $20$ more questions than the first, so it had $x+20$ questions total, and she answered $80\%$ of them correctly:

• Number correct on the second exam is

Both expressions represent the same number of correct answers on the second exam, so set them equal:

Solve step by step:

Now solve for $x$ by dividing both sides by $0.1$.

From $0.1x = 16$,

Check:

• First exam: $0.75 \cdot 160 = 120$ correct.
• Second exam: $20\%$ more correct than 120 is $1.2 \cdot 120 = 144$.
• Second exam total questions: $160 + 20 = 180$, and $80\%$ of 180 is $0.8 \cdot 180 = 144$.

Both descriptions match, so the first exam had 160 questions.