To determine the total number of questions [tex]\( q \)[/tex] on Tim's math test, let's approach this problem step by step.
1. Identify the number of questions Tim got correct:
- Tim got 10 answers wrong, which means he answered [tex]\( q - 10 \)[/tex] questions correctly, where [tex]\( q \)[/tex] is the total number of questions.
2. Points per correct answer:
- Tim received 4 points for each correct answer.
3. Total points scored:
- Tim's score was 76 points. This score came solely from his correct answers.
4. Set up the equation:
- The total points scored can be expressed by multiplying the number of correct answers by the points per correct answer:
[tex]\[
4 \times (q - 10) = 76
\][/tex]
5. Solve for [tex]\( q \)[/tex]:
- First, isolate the term with [tex]\( q \)[/tex] by dividing both sides of the equation by 4:
[tex]\[
q - 10 = \frac{76}{4}
\][/tex]
- We can calculate:
[tex]\[
\frac{76}{4} = 19
\][/tex]
- Now, add 10 to both sides to solve for [tex]\( q \)[/tex]:
[tex]\[
q = 19 + 10
\][/tex]
- This simplifies to:
[tex]\[
q = 29
\][/tex]
6. Final Result:
- Therefore, the total number of questions on Tim's math test is [tex]\( q \)[/tex]:
[tex]\[
\boxed{29} \text{ questions}
\][/tex]
