At Fairview Middle School, 75 ?band members need to raise a total of $8,250 ?for a trip. So far, they have raised $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 ?each. A local business agrees to donate an additional $0.50 ?for each $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?
The Correct Answer and Explanation is :
Part A: How much money, in dollars, per band member, still needs to be raised for the trip?
To determine how much money is still needed, we subtract the amount already raised from the total amount needed:
Total amount needed: $8,250
Amount already raised: $3,120
Remaining amount needed = $8,250 – $3,120 = $5,130
Now, to find out how much money still needs to be raised per band member, we divide the remaining amount by the number of band members (75):
Amount per band member = $5,130 ÷ 75 = $68.40
So, each band member still needs to raise $68.40.
Part B: The least number of concert tickets the band must sell to raise the rest of the money.
The remaining amount needed for the trip is $5,130. Tickets for the concert will be sold at $7.50 each, and for every $1.00 in ticket sales, a local business will donate an additional $0.50.
The total amount raised from ticket sales and donations will be the ticket price ($7.50) plus the donation from the business. Since the donation is 50% of the ticket price, the total raised per ticket will be:
Total raised per ticket = $7.50 + (0.50 × 7.50) = $7.50 + $3.75 = $11.25
Now, to find out how many tickets need to be sold to raise the remaining $5,130, divide the remaining amount by the total raised per ticket:
Number of tickets = $5,130 ÷ $11.25 ≈ 456
Therefore, the band must sell at least 456 tickets to raise the remaining money.
Explanation:
The problem involves two main calculations: first, finding out how much money per band member still needs to be raised, and second, determining how many concert tickets must be sold to raise the remaining funds.
In Part A, we subtract the amount already raised from the total needed and then divide the remaining funds by the number of band members to find how much each member still needs to contribute.
In Part B, we calculate the combined earnings from ticket sales and business donations, which gives us a total amount per ticket. Dividing the remaining amount to be raised by this value helps us determine the least number of tickets the band must sell to meet their fundraising goal.
The approach relies on basic arithmetic operations such as subtraction, division, and multiplication to solve the problem efficiently.