A farmer sets up two corn mazes for a fall festival, as shown in this model.

Question

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)

Answer 1

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)