Bob received 6 points for each question he answered correctly on Part 1 of a test and 4 points for each question he answered correctly on Part 2. If he answered 33 questions correctly and received a total of 168 points, how many questions did he answer correctly on Part 1?

Same as the bike problem.

If he answered correctly all part 2 (4 points each) questions, then he would have got 4*33=132 points. Since he got 168 points, he got 168-132=36 points left over. Since part 1 questions has 2 points more each, he must have got 36/2=18 part 1 questions, and 33-18=15 part 2 questions.

You can also do this using system of equations if you have a pen and paper.

To solve this problem, let's use algebra.

Let's assume that Bob answered x questions correctly on Part 1. Since he received 6 points for each question answered correctly on Part 1, the total points he received on Part 1 would be 6x.

Similarly, let's assume that Bob answered y questions correctly on Part 2. Since he received 4 points for each question answered correctly on Part 2, the total points he received on Part 2 would be 4y.

According to the problem, Bob answered 33 questions correctly in total. Therefore, the total number of questions he answered on both parts is x + y = 33.

The total points he received is given as 168, so we can write the equation 6x + 4y = 168.

Now we can solve this system of equations.

Substituting x + y = 33 into the equation 6x + 4y = 168, we get:
6x + 4(33 - x) = 168.

Simplifying this equation, we have:
6x + 132 - 4x = 168,
2x + 132 = 168,
2x = 168 - 132,
2x = 36,
x = 36 / 2,
x = 18.

Therefore, Bob answered 18 questions correctly on Part 1.