John participated in a game where each participant was asked to pick up six cards from a box without looking at the cards. The participant with the highest total would be declared the winner. Each card had a numerical value from one to a hundred written on it. John's average in the first four cards came out to be 83.What is the lowest he can get in the sixth draw so that he still has a chance of taking his overall average to at least 88 ?

Options

A. 100
B. 98
C. 96
D. 92

Answer

To solve the problem step-by-step, we will follow these calculations:

### Step 1: Calculate the total score from the first four cards.
Since John's average score for the first four cards is 83, we can find the total score by multiplying the average by the number of cards.

\[ \text{Total score from first four cards} = \text{Average} \times \text{Number of cards} = 83 \times 4 = 332 \]

### Step 2: Determine the requirement for the overall average.
John wants to achieve an overall average of at least 88 after drawing six cards. Therefore, the total score required for six cards can be calculated as follows:

\[ \text{Total score required for six cards} = \text{Average} \times \text{Number of cards} = 88 \times 6 = 528 \]

### Step 3: Set up the equation for the total score.
Let \( x \) be the score of the sixth card. The total score from all six cards can be expressed as:

\[ \text{Total score} = \text{Score from first four cards} + \text{Score from fifth card} + \text{Score from sixth card} \]
\[ 528 = 332 + 100 + x \]

### Step 4: Simplify the equation.
Now, we can simplify the equation to find \( x \):

\[ 528 = 432 + x \]

### Step 5: Solve for \( x \).
Subtract 432 from both sides to isolate \( x \):

\[ x = 528 - 432 = 96 \]

### Conclusion:
John needs to score at least 96 in the sixth draw to achieve an overall average of at least 88.