At Fairview Middle School,

Question

75
75 band members need to raise a total of
$
8
,
250
$8,250 for a trip. So far, they have raised
$
3
,
120
$3,120.
​How much money, in dollars, per band member, still needs to be raised for the trip?

​Enter your answer in the box.

​Part B

The entire band decides to have a concert to raise the money for the trip. Tickets for the concert will cost
$
7.50
$7.50 each. A local business agrees to donate an additional
$
0.50
$0.50 for each
$
1.00
$1.00 in ticket sales to the band for their trip.

​

What is the least number of concert tickets the band must sell in order to raise the rest of the money needed for the trip?

​Enter your answer in the box.

Answer 1

To solve this problem, we can break it down into steps.

Part A

1. Determine the total amount still needed for the trip: \[ \text{Total amount needed} = 8250 \quad \text{(total cost)} \] \[ \text{Amount already raised} = 3120 \] \[ \text{Amount still needed} = 8250 - 3120 = 5130 \]

2. Calculate how much each band member needs to raise: \[ \text{Number of band members} = 75 \] \[ \text{Amount per band member} = \frac{5130}{75} = 68.4 \]

Thus, each band member needs to raise $68.40.

Part B

1. Determine how much money is raised per ticket sold:

   • Each ticket costs $7.50.
   • For every $1.00 in ticket sales, a local business donates $0.50.
   • Therefore, the total raised for every $1.00 in ticket sales is $1.50.
   • We will calculate how much is raised from one ticket: \[ \text{Amount raised per ticket} = 7.50 + \left(0.50 \times \frac{7.50}{1.00}\right) = 7.50 + 3.75 = 11.25 \]

2. Determine the amount that needs to be raised: The total amount still needed is $5,130.

3. Calculate the number of tickets needed to be sold: \[ \text{Number of tickets needed} = \frac{5130}{11.25} \approx 456 \] Since they cannot sell a fraction of a ticket, we round up to the nearest whole number: \[ \text{Minimum number of tickets to sell} = 456 \]

Thus, the least number of concert tickets the band must sell is 456.