A farmer plants corn and soybeans. This model shows the area reserved for each.

Question

Corn:
20 acres
Soybeans:
12 acres
Which expression is equivalent to the sum of the two areas?
(1 point)
(4 + 5) (4 + 3)
4(5 + 3)
4(5) (3)
5(4+3)

Answer 1

To find the expression that is equivalent to the sum of the areas reserved for corn and soybeans, we need to add the areas together.

The area for corn is 20 acres and the area for soybeans is 12 acres.

The sum of these areas is:

\( 20 + 12 = 32 \) acres.

Now, let’s see which of the provided expressions, when simplified, equals 32.

1. (4 + 5)(4 + 3):

   • This simplifies to \( 9 \times 7 = 63 \).

2. 4(5 + 3):

   • This simplifies to \( 4 \times 8 = 32 \).

3. 4(5)(3):

   • This simplifies to \( 4 \times 5 \times 3 = 60 \).

4. 5(4 + 3):

   • This simplifies to \( 5 \times 7 = 35 \).

Among these options, 4(5 + 3) is the only expression that equals 32 acres.

Thus, the equivalent expression for the sum of the two areas is 4(5 + 3).