Question
A rectangular garden has a length that is a times its width. If the perimeter of the garden is 24 meters, express
the width of the garden in terms of a . Round your answer to two decimal places if necessary. Width = ____
meters
2. The cost of producing x items is given by the equation C = bx + 500 , where b is the cost per item and 500 is a
fixed cost. If the total cost of producing 100 items is $2000, which of the following statements is true?
A. The cost per item (
b ) is $20
C. The fixed cost
should be $1000 for
the equation to be
true
B. The cost per item (
b ) is $15
D. It’s impossible to
determine the cost
per item without more
information
3. A charity organization has a fundraising goal of $10,000. They receive a large donation of $2,500 and then plan
to sell raffle tickets. If they sell x tickets at y dollars each, write an inequality to represent this situation. Then,
explain what the solution to this inequality would mean in the context of their fundraising efforts.
the width of the garden in terms of a . Round your answer to two decimal places if necessary. Width = ____
meters
2. The cost of producing x items is given by the equation C = bx + 500 , where b is the cost per item and 500 is a
fixed cost. If the total cost of producing 100 items is $2000, which of the following statements is true?
A. The cost per item (
b ) is $20
C. The fixed cost
should be $1000 for
the equation to be
true
B. The cost per item (
b ) is $15
D. It’s impossible to
determine the cost
per item without more
information
3. A charity organization has a fundraising goal of $10,000. They receive a large donation of $2,500 and then plan
to sell raffle tickets. If they sell x tickets at y dollars each, write an inequality to represent this situation. Then,
explain what the solution to this inequality would mean in the context of their fundraising efforts.
Answers
GPT-5 mini
1) Let the width be w and the length be a·w. Perimeter: 2(length + width) = 24 → 2(aw + w) = 24 → 2w(a+1) = 24 → w(a+1) = 12.
Width = 12/(a + 1) meters. (Round to two decimals only if you substitute a numeric value.)
2) C = bx + 500. For x = 100 and C = 2000: 2000 = 100b + 500 → 100b = 1500 → b = 15.
Answer: B. The cost per item is $15.
3) They already have $2,500, so ticket revenue xy must make up the rest to reach $10,000:
2500 + xy ≥ 10000 → xy ≥ 7500.
Interpretation: the number of tickets times the price per ticket must be at least $7,500. For a given ticket price y, they must sell at least x ≥ 7500/y tickets (and x should be a nonnegative integer).
Width = 12/(a + 1) meters. (Round to two decimals only if you substitute a numeric value.)
2) C = bx + 500. For x = 100 and C = 2000: 2000 = 100b + 500 → 100b = 1500 → b = 15.
Answer: B. The cost per item is $15.
3) They already have $2,500, so ticket revenue xy must make up the rest to reach $10,000:
2500 + xy ≥ 10000 → xy ≥ 7500.
Interpretation: the number of tickets times the price per ticket must be at least $7,500. For a given ticket price y, they must sell at least x ≥ 7500/y tickets (and x should be a nonnegative integer).