Question

On a game show, a contestant receives 15 points for each correct answer and 0 points for each incorrect answer. At the end of the
1st round, Jackie had 90 points. At the end of the
2nd round, Jackie had a grand total of 135
points.

How many questions did Jackie answer correctly in the
2nd round?

Answer 1

To solve for the number of questions Jackie answered correctly in the second round, we can begin by breaking down Jackie’s performance in the two rounds.

In the first round, Jackie scored a total of 90 points. Since she earns 15 points for each correct answer, we can let \( c_1 \) represent the number of correct answers in the first round. The equation for the points from the first round can be expressed as:

\[
15 c_1 = 90
\]

Dividing both sides by 15 gives:

\[
c_1 = \frac{90}{15} = 6
\]

Thus, Jackie answered 6 questions correctly in the first round.

Now, at the end of the second round, Jackie had a total of 135 points. Since she started the second round with 90 points, the points scored in the second round can be calculated as follows:

\[
\text{Points scored in the 2nd round} = 135 - 90 = 45
\]

Let \( c_2 \) be the number of correct answers Jackie provided in the second round. The points scored in the second round can also be expressed as:

\[
15 c_2 = 45
\]

Dividing both sides by 15 gives:

\[
c_2 = \frac{45}{15} = 3
\]

Thus, Jackie answered **3 questions** correctly in the second round. So the answer is:

\[
\boxed{3}
\]