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
st round, Jackie had 2 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?
st round, Jackie had 2 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?
Answers
GPT-4o mini
To determine how many questions Jackie answered correctly in the 2nd round, we can follow these steps:
1. **Identify Jackie’s performance in the 1st round:**
Let \( c_1 \) be the number of correct answers in the 1st round. Jackie earns 15 points for each correct answer.
The points Jackie earned in the 1st round can be expressed as:
\[
\text{Points}_{1st \ round} = 15c_1
\]
At the end of the 1st round, Jackie had 2 points:
\[
15c_1 = 2
\]
From this, we can see that there can’t be a non-negative integer \( c_1 \) that satisfies it, indicating Jackie likely had a penalty or rule variation (since points are usually whole numbers and Jackie's points should reflect this).
However, given a point (2) that comes after points, we focus on total points after the second round.
2. **Identify Jackie’s performance in the 2nd round:**
Let \( c_2 \) be the number of correct answers in the 2nd round, and \( i_2 \) be the number of incorrect answers. The total points from the 2nd round is:
\[
\text{Points}_{2nd \ round} = 15c_2
\]
The total points after the 2nd round are given to be 135:
\[
2 + 15c_2 = 135
\]
3. **Calculate points in the 2nd round:**
Rearranging the equation:
\[
15c_2 = 135 - 2
\]
\[
15c_2 = 133
\]
\[
c_2 = \frac{133}{15}
\]
This results in:
\[
c_2 = 8.8667
\]
Since \( c_2 \) must be a whole number, it won't be meaningful per integrity of odd points received.
Then you might reconsider possible error or missvalue in describing rounds or ask for real total point calculation.
Overall, logically tracing valid base math from game show without fractional points (as each answer must relate back to whole points), Jackie couldn't have gained any proper integer-based return from rounds described through stated values of points. Thus, if 135 allowed false notations, your setup may require reevaluation of actual game round rules or initialize with integer solutions based on input mismatch.
If zero/non-answer from possibly dealt penalties remains, Jackie \ensuremath{c_2} might resolve around basic trusted point incomes. Please check the statements/rules for rethink via whole performance, wrong clues in incremental rounds changing sums or facing penalties gain on specific choices as needed. Checking input/outlay might adjust the 0/15 round statements too.
1. **Identify Jackie’s performance in the 1st round:**
Let \( c_1 \) be the number of correct answers in the 1st round. Jackie earns 15 points for each correct answer.
The points Jackie earned in the 1st round can be expressed as:
\[
\text{Points}_{1st \ round} = 15c_1
\]
At the end of the 1st round, Jackie had 2 points:
\[
15c_1 = 2
\]
From this, we can see that there can’t be a non-negative integer \( c_1 \) that satisfies it, indicating Jackie likely had a penalty or rule variation (since points are usually whole numbers and Jackie's points should reflect this).
However, given a point (2) that comes after points, we focus on total points after the second round.
2. **Identify Jackie’s performance in the 2nd round:**
Let \( c_2 \) be the number of correct answers in the 2nd round, and \( i_2 \) be the number of incorrect answers. The total points from the 2nd round is:
\[
\text{Points}_{2nd \ round} = 15c_2
\]
The total points after the 2nd round are given to be 135:
\[
2 + 15c_2 = 135
\]
3. **Calculate points in the 2nd round:**
Rearranging the equation:
\[
15c_2 = 135 - 2
\]
\[
15c_2 = 133
\]
\[
c_2 = \frac{133}{15}
\]
This results in:
\[
c_2 = 8.8667
\]
Since \( c_2 \) must be a whole number, it won't be meaningful per integrity of odd points received.
Then you might reconsider possible error or missvalue in describing rounds or ask for real total point calculation.
Overall, logically tracing valid base math from game show without fractional points (as each answer must relate back to whole points), Jackie couldn't have gained any proper integer-based return from rounds described through stated values of points. Thus, if 135 allowed false notations, your setup may require reevaluation of actual game round rules or initialize with integer solutions based on input mismatch.
If zero/non-answer from possibly dealt penalties remains, Jackie \ensuremath{c_2} might resolve around basic trusted point incomes. Please check the statements/rules for rethink via whole performance, wrong clues in incremental rounds changing sums or facing penalties gain on specific choices as needed. Checking input/outlay might adjust the 0/15 round statements too.