Question
1. A local charity is organizing a fundraising event. They plan to sell tickets for $15 each and expect to have x
attendees. Their goal is to raise at least $3000. Write an inequality to represent this situation, and solve it to
find the minimum number of attendees needed: ____ attendees.
2. The formula for the volume of a cylinder is V = πr2h , where V is the volume, r is the radius of the base, and
h is the height. If you want to find the height of a cylinder given its volume and radius, which of the following
correctly represents the rearranged formula?
A. h =
V
πr^2
C. h = V − πr^2
B. h =
V
πr
D. h =
V −πr^2
r
3. A rectangular swimming pool is being constructed in a community park. The length of the pool is 3 meters more
than twice its width. The perimeter of the pool is 50 meters. Set up and solve a system of equations to find the
dimensions of the pool. Show all your work and explain your reasoning for each step.
attendees. Their goal is to raise at least $3000. Write an inequality to represent this situation, and solve it to
find the minimum number of attendees needed: ____ attendees.
2. The formula for the volume of a cylinder is V = πr2h , where V is the volume, r is the radius of the base, and
h is the height. If you want to find the height of a cylinder given its volume and radius, which of the following
correctly represents the rearranged formula?
A. h =
V
πr^2
C. h = V − πr^2
B. h =
V
πr
D. h =
V −πr^2
r
3. A rectangular swimming pool is being constructed in a community park. The length of the pool is 3 meters more
than twice its width. The perimeter of the pool is 50 meters. Set up and solve a system of equations to find the
dimensions of the pool. Show all your work and explain your reasoning for each step.
Answers
Answered by
GPT-5 mini
1) Let x = number of attendees. Revenue = 15x. They want at least $3000, so
15x ≥ 3000.
Solve: x ≥ 3000/15 = 200.
Minimum number of attendees: 200 attendees.
2) Start from V = π r^2 h. Solve for h by dividing both sides by π r^2:
h = V / (π r^2).
Answer: A.
3) Let w = width (m). Length L is "3 meters more than twice its width": L = 2w + 3.
Perimeter of a rectangle: P = 2(L + w). Given P = 50, so
2(L + w) = 50.
Substitute L = 2w + 3:
2((2w + 3) + w) = 50
2(3w + 3) = 50
6w + 6 = 50
6w = 44
w = 44/6 = 22/3 ≈ 7.33 m.
Now find L:
L = 2w + 3 = 2(22/3) + 3 = 44/3 + 3 = 44/3 + 9/3 = 53/3 ≈ 17.67 m.
Dimensions: width = 22/3 m (≈7.33 m), length = 53/3 m (≈17.67 m).
15x ≥ 3000.
Solve: x ≥ 3000/15 = 200.
Minimum number of attendees: 200 attendees.
2) Start from V = π r^2 h. Solve for h by dividing both sides by π r^2:
h = V / (π r^2).
Answer: A.
3) Let w = width (m). Length L is "3 meters more than twice its width": L = 2w + 3.
Perimeter of a rectangle: P = 2(L + w). Given P = 50, so
2(L + w) = 50.
Substitute L = 2w + 3:
2((2w + 3) + w) = 50
2(3w + 3) = 50
6w + 6 = 50
6w = 44
w = 44/6 = 22/3 ≈ 7.33 m.
Now find L:
L = 2w + 3 = 2(22/3) + 3 = 44/3 + 3 = 44/3 + 9/3 = 53/3 ≈ 17.67 m.
Dimensions: width = 22/3 m (≈7.33 m), length = 53/3 m (≈17.67 m).