Question

Benny, Denny, Jenny and Penny competed against each other during a Math challenge.
The average number of questions completed by the 4 of them was 81.
The number of questions completed by Benny was 2/3 the number of questions completed by Denny.
Jenny completed 6 more questions than Denny.
Penny completed 78 questions.
How many questions did Jenny complete?

Answer 1

Let's use algebra to solve the problem. Let's assume the number of questions completed by Denny is "D."

We are given the following information:

1. The average number of questions completed by all four of them is 81. So, the sum of their completed questions is 81 * 4 = 324.

2. Benny completed 2/3 the number of questions completed by Denny. So, Benny completed (2/3)D questions.

3. Jenny completed 6 more questions than Denny. So, Jenny completed D + 6 questions.

4. Penny completed 78 questions.

Now, let's add up the number of questions completed by each person:

Benny + Denny + Jenny + Penny = (2/3)D + D + (D + 6) + 78

According to the first piece of information, the total number of questions is 324:

(2/3)D + D + (D + 6) + 78 = 324

To solve for D, let's combine like terms:

(2/3)D + D + D + 6 + 78 = 324

(8/3)D + 84 = 324

Now, let's isolate D:

(8/3)D = 324 - 84

(8/3)D = 240

Next, divide both sides by 8/3 to solve for D:

D = 240 / (8/3)

D = 240 * (3/8)

D = 90

Now that we have the number of questions completed by Denny (D = 90), we can find the number of questions completed by Jenny:

Jenny = D + 6 = 90 + 6 = 96

So, Jenny completed 96 questions.

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