Question
A farmer sets up two corn mazes for a fall festival, as shown in this model.
A model with 2 corn mazes. Corn maze 1 is made up of 5 acres represented by 1 row of 5. Corn maze 2 is made up of 15 acres represented by 3 rows of 5.
Which equivalent expressions are represented by the model? Check all that apply.
15 + 5
3 + (5 + 1)
3(5 + 1)
5(3 + 1)
(5)(3) + (5)(1)
A model with 2 corn mazes. Corn maze 1 is made up of 5 acres represented by 1 row of 5. Corn maze 2 is made up of 15 acres represented by 3 rows of 5.
Which equivalent expressions are represented by the model? Check all that apply.
15 + 5
3 + (5 + 1)
3(5 + 1)
5(3 + 1)
(5)(3) + (5)(1)
Answers
GPT-4o mini
To analyze the expressions and their equivalences in the context of the farmer's corn mazes, we first note the sizes of corn maze 1 and corn maze 2:
1. **Corn maze 1**: 5 acres (1 row of 5).
2. **Corn maze 2**: 15 acres (3 rows of 5).
Now we can represent these sizes mathematically:
- Corn maze 1 = 5 acres
- Corn maze 2 = 3 rows of 5 acres = \( 3 \times 5 = 15 \) acres
Now, let's evaluate the given expressions in terms of equivalence to the combined total of these corn mazes:
1. **15 + 5**: This represents a total of 20 acres, which does not directly correspond to the sizes of the mazes.
- Not equivalent.
2. **3 + (5 + 1)**: This simplifies to \( 3 + 6 = 9 \). This does not correspond to the sizes of the mazes.
- Not equivalent.
3. **3(5 + 1)**: This expands to \( 3 \times 6 = 18 \). This does not match 20 acres.
- Not equivalent.
4. **5(3 + 1)**: This expands to \( 5 \times 4 = 20 \). This matches the total acreage of both mazes (5 + 15).
- Equivalent.
5. **(5)(3) + (5)(1)**: This expands to \( 15 + 5 = 20 \). This also matches the total acreage.
- Equivalent.
From the analysis, the expressions that are equivalent to the model of the corn mazes are:
- **5(3 + 1)**
- **(5)(3) + (5)(1)**
1. **Corn maze 1**: 5 acres (1 row of 5).
2. **Corn maze 2**: 15 acres (3 rows of 5).
Now we can represent these sizes mathematically:
- Corn maze 1 = 5 acres
- Corn maze 2 = 3 rows of 5 acres = \( 3 \times 5 = 15 \) acres
Now, let's evaluate the given expressions in terms of equivalence to the combined total of these corn mazes:
1. **15 + 5**: This represents a total of 20 acres, which does not directly correspond to the sizes of the mazes.
- Not equivalent.
2. **3 + (5 + 1)**: This simplifies to \( 3 + 6 = 9 \). This does not correspond to the sizes of the mazes.
- Not equivalent.
3. **3(5 + 1)**: This expands to \( 3 \times 6 = 18 \). This does not match 20 acres.
- Not equivalent.
4. **5(3 + 1)**: This expands to \( 5 \times 4 = 20 \). This matches the total acreage of both mazes (5 + 15).
- Equivalent.
5. **(5)(3) + (5)(1)**: This expands to \( 15 + 5 = 20 \). This also matches the total acreage.
- Equivalent.
From the analysis, the expressions that are equivalent to the model of the corn mazes are:
- **5(3 + 1)**
- **(5)(3) + (5)(1)**