Question
Part 1: At the State Fair it costs $2.75 for a piece of pizza and $3.50 for a funnel cake. Set up an algebraic expression to find the total cost when buying "p" pieces of pizza and "f" funnel cakes.
Answers
GPT-4o mini
To set up an algebraic expression for the total cost when buying "p" pieces of pizza and "f" funnel cakes, you can use the following steps:
1. Determine the cost for "p" pieces of pizza. Since each piece of pizza costs $2.75, the cost for "p" pieces is:
\[
2.75p
\]
2. Determine the cost for "f" funnel cakes. Since each funnel cake costs $3.50, the cost for "f" funnel cakes is:
\[
3.50f
\]
3. To find the total cost (C), you add both costs together:
\[
C = 2.75p + 3.50f
\]
So, the algebraic expression for the total cost is:
\[
C = 2.75p + 3.50f
\]
1. Determine the cost for "p" pieces of pizza. Since each piece of pizza costs $2.75, the cost for "p" pieces is:
\[
2.75p
\]
2. Determine the cost for "f" funnel cakes. Since each funnel cake costs $3.50, the cost for "f" funnel cakes is:
\[
3.50f
\]
3. To find the total cost (C), you add both costs together:
\[
C = 2.75p + 3.50f
\]
So, the algebraic expression for the total cost is:
\[
C = 2.75p + 3.50f
\]
QUAAACK
Part 2: You and your three friends decide to order 2 pieces of pizza and 1 funnel cake each. Using the information from Part 1, solve to find out how much it would cost for your AND your friends to order 2 pieces of pizza and 1 funnel cake each. Show all of your steps!
GPT-4o mini
To find the total cost for you and your three friends to order 2 pieces of pizza and 1 funnel cake each, follow these steps:
1. **Determine the number of total people**: You and your three friends make a total of 4 people.
2. **Find the total order for each person**:
- Each person orders 2 pieces of pizza.
- Each person also orders 1 funnel cake.
3. **Calculate the total pieces of pizza and funnel cakes for all 4 people**:
- Total pieces of pizza = 2 pieces/person × 4 people = \( 2 \times 4 = 8 \) pieces of pizza.
- Total funnel cakes = 1 funnel cake/person × 4 people = \( 1 \times 4 = 4 \) funnel cakes.
4. **Use the algebraic expression from Part 1 to find the total cost**:
- Using the expression \( C = 2.75p + 3.50f \):
\[
p = 8 \quad \text{(total pieces of pizza)}
\]
\[
f = 4 \quad \text{(total funnel cakes)}
\]
5. **Substitute the values into the expression**:
\[
C = 2.75(8) + 3.50(4)
\]
6. **Calculate the cost for the pizza**:
\[
2.75 \times 8 = 22.00
\]
7. **Calculate the cost for the funnel cakes**:
\[
3.50 \times 4 = 14.00
\]
8. **Add the two costs together to find the total cost**:
\[
C = 22.00 + 14.00 = 36.00
\]
Therefore, the total cost for you and your three friends to order 2 pieces of pizza and 1 funnel cake each is **$36.00**.
1. **Determine the number of total people**: You and your three friends make a total of 4 people.
2. **Find the total order for each person**:
- Each person orders 2 pieces of pizza.
- Each person also orders 1 funnel cake.
3. **Calculate the total pieces of pizza and funnel cakes for all 4 people**:
- Total pieces of pizza = 2 pieces/person × 4 people = \( 2 \times 4 = 8 \) pieces of pizza.
- Total funnel cakes = 1 funnel cake/person × 4 people = \( 1 \times 4 = 4 \) funnel cakes.
4. **Use the algebraic expression from Part 1 to find the total cost**:
- Using the expression \( C = 2.75p + 3.50f \):
\[
p = 8 \quad \text{(total pieces of pizza)}
\]
\[
f = 4 \quad \text{(total funnel cakes)}
\]
5. **Substitute the values into the expression**:
\[
C = 2.75(8) + 3.50(4)
\]
6. **Calculate the cost for the pizza**:
\[
2.75 \times 8 = 22.00
\]
7. **Calculate the cost for the funnel cakes**:
\[
3.50 \times 4 = 14.00
\]
8. **Add the two costs together to find the total cost**:
\[
C = 22.00 + 14.00 = 36.00
\]
Therefore, the total cost for you and your three friends to order 2 pieces of pizza and 1 funnel cake each is **$36.00**.