Question

Liam and his friends are hosting a bake sale to raise funds for their school trip. They decided to sell cookies for $3 each and muffins for $5 each. Their goal is to raise at least $300, but they want to sell no more than 80 items in total. Select one of the following combinations that Liam can sell to make at least $300 while keeping the total items sold to a maximum of 80:

Answer 1

To meet their goal of raising at least $300 while selling no more than 80 items, we can represent the number of cookies sold as \( c \) and the number of muffins sold as \( m \). We need to satisfy the following conditions:

1. Total revenue: \( 3c + 5m \geq 300 \)
2. Total items: \( c + m \leq 80 \)

Let’s go through some possible combinations of cookies and muffins:

1. Combination A: \( c = 50, m = 30 \)

   • Total items: \( 50 + 30 = 80 \) (this is within the limit)
   • Total revenue: \( 3(50) + 5(30) = 150 + 150 = 300 \) (this meets the revenue target)

2. Combination B: \( c = 20, m = 70 \)

   • Total items: \( 20 + 70 = 90 \) (this exceeds the limit)

3. Combination C: \( c = 40, m = 40 \)

   • Total items: \( 40 + 40 = 80 \) (this is within the limit)
   • Total revenue: \( 3(40) + 5(40) = 120 + 200 = 320 \) (this meets the revenue target)

4. Combination D: \( c = 0, m = 60 \)

   • Total items: \( 0 + 60 = 60 \) (this is within the limit)
   • Total revenue: \( 3(0) + 5(60) = 0 + 300 = 300 \) (this meets the revenue target)

Each of these combinations (A, C, and D) successfully achieves at least $300 in revenue while keeping the total items sold within the limit of 80. Any of these could be viable options for Liam's bake sale. If you provide specific combinations to choose from, I can also analyze those.