given the equation 8(n+6)=104 identify the real-word problem that corresponds to this equation

Answer 1

The equation \(8(n + 6) = 104\) can represent a variety of real-world situations, but let's construct a scenario around it.

Problem Context:

Imagine you are organizing a group activity where each participant needs to pay a registration fee to cover the costs of the event. The cost breakdown is as follows:

1. There are 8 participants.
2. Each participant is responsible for paying a certain fee (\(n\)) plus an additional $6 (this could represent a fixed cost such as venue rental or materials).
3. The total amount collected from all participants is $104.

Real-World Problem:

"Suppose you are organizing a community workshop that costs $104 to run. You have 8 participants signed up, and each participant needs to contribute an equal base fee plus an additional $6 to cover extra costs. How much is the base fee each participant needs to pay?"

In this case, the variable \(n\) represents the base registration fee each participant has to pay.

To solve for \(n\):

1. Distribute the 8: \[ 8n + 48 = 104 \]

2. Subtract 48 from both sides: \[ 8n = 56 \]

3. Divide by 8: \[ n = 7 \]

So, each participant would pay $7 as the base fee, plus $6, which totals $13 per participant.