To determine the total number of problems on the test, let's denote the total number of problems as $x$.

According to the problem:

• Sam got 64% of the problems correct.
• Therefore, he got $100\% - 64\% = 36\%$ of the problems wrong.
• He had 18 problems wrong, which is 36% of the total problems.

So we can set up the equation: $0.36 \times x = 18$

Now, solve for $x$: $x = \frac{18}{0.36}$ $x = 50$

So, there were 50 problems on the test.

Would you like further explanation on this problem or have any other questions?

Here are some related questions that might interest you:

1. What would Sam's score be if he got 20 problems wrong instead?
2. How can you calculate the total problems if you only know the correct percentage and the number of incorrect answers?
3. What would the percentage of correct answers be if Sam missed only 10 problems?
4. How would you find the number of correct answers if you know the total problems and the score percentage?
5. How could this problem be approached differently, for instance, by considering correct answers rather than incorrect?

Tip: Remember, when given percentages and partial results, setting up an equation with the percentage as a decimal often makes calculations straightforward.