A hotel charges $20 for the use of its dining room plus $2.50 for each lunch. An association is using the hotel for a meeting and charges its members $3 per person to attend. Four non-paying members are invited as honorees. How many paying members must attend in order for the association to meet its expenses?
20+2.50(x+4)=3x
If you solve for x you get 60
If there are p paying members, their fees ($3 each) must cover the costs (including the 4 meals for the guests):
3p = 20 + 2.5p + 4*2.5
p = 60
Well, let's crunch some numbers, but don't worry, I won't crunch any biscuits. We have a hotel charging $20 for the use of the dining room, and $2.50 for each lunch. The association is charging its members $3 per person to attend, and they have invited four non-paying members as honorees. So, let's figure out how many paying members are needed.
The expenses the association needs to cover are the dining room charge and the lunches. The dining room charge is $20, and for each paying member, there's an additional $2.50 for lunch. Since the non-paying members (honorees) won't contribute towards the expenses, we don't need to consider them.
Let's say the number of paying members needed is "x". The equation to represent the expenses is:
20 + 2.50x = 3x
Now, let's solve it:
20 = 0.50x
x = 40
So, in order for the association to meet its expenses, at least 40 paying members must attend. But hey, the more, the merrier!
To determine the number of paying members needed for the association to meet its expenses, we need to calculate the total expenses and then divide it by the cost per person.
Let's break down the expenses:
1. Dining room charge: $20
2. Lunch charge per paying member: $2.50
3. Cost per attending member: $3
4. Non-paying honorees: 4
The total cost per attending member is calculated as follows:
Cost per attending member = Dining room charge + Lunch charge per paying member + Cost per attending member
= $20 + $2.50 + $3
= $25.50
To find the number of paying members needed, we divide the total expenses by the cost per attending member:
Number of paying members needed = Total expenses / Cost per attending member
Since the only additional expense is for lunch, we can disregard the dining room charge. Thus, the total expenses would be the cost per attending member:
Number of paying members needed = $25.50 / $3
≈ 8.5
To meet its expenses, the association would need approximately 8.5 paying members to attend. However, since we cannot have partial attendees, the association would need at least 9 paying members to cover the costs.
To determine the number of paying members required to meet the association's expenses, we need to calculate the total expenses and divide it by the cost per paying member.
First, let's break down the expenses:
1. The hotel charges a fixed fee of $20 for the use of its dining room.
2. Each lunch costs $2.50 per person attending the meeting.
3. The association charges its members $3 per person attending the meeting.
4. Four non-paying members are invited as honorees.
To calculate the total cost, we can multiply the number of lunches by the cost per lunch and add the fixed fee for the dining room.
Let's assign some variables:
- P = Number of paying members attending the meeting
- N = Total number of attendees (paying and non-paying)
- L = Number of lunches ordered (equal to N - 4, as the non-paying members don't have lunch)
Now let's calculate the total expenses:
Total expenses = Cost of dining room + (Number of lunches × Cost per lunch) + Cost per paying member × Number of paying members
= $20 + ($2.50 × (N - 4)) + ($3 × P)
Since the association wants to meet its expenses, the total revenue from paying members should be equal to the total expenses, so we can set up the equation like this:
$3 × P = $20 + ($2.50 × (P + 4))
Now, we can solve for P:
$3 × P = $20 + ($2.50 × P) + ($2.50 × 4)
$3 × P = $20 + ($2.50 × P) + $10
$3 × P - ($2.50 × P) = $30
$0.50 × P = $30
P = $30 / $0.50
P = 60
Therefore, the association must have 60 paying members attend the meeting in order to meet its expenses.